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This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

The general form of a quadratic equation is \(ax^2+bx+c=0\). It's roots are: \(x_1=\frac{-b-\sqrt{b^2-4ac}}{2a}\) and \(x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}\)

Expression \(b^2-4ac\) is called discriminant:

If discriminant is positive quadratics has two roots;

If discriminant is negative quadratics has no root;

If discriminant is zero quadratics has one root.

When graphed quadratic expression (\(ax^2+bx+c=0\)) gives parabola:

The larger the absolute value of \(a\), the steeper (or thinner) the parabola is, since the value of y is increased more quickly.

If \(a\) is positive, the parabola opens upward, if negative, the parabola opens downward.

Viete's theorem

Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).

Common mistake to avoid Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

For example, \(xy=y\) cannot be reduced by \(y\) because \(y\) could be 0 and we cannot divide by 0. If we do we'll loose one of the solutions. The correct way is: \(xy=y\) --> \(xy-y=0\) --> \(y(x-1)=0\) --> \(y=0\) or \(x=1\).

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

The general form of a quadratic equation is \(ax^2+bx+c=0\). It's roots are: \(x_1=\frac{-b-\sqrt{b^2-4ac}}{2a}\) and \(x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}\)

Expression \(b^2-4ac\) is called discriminant:

If discriminant is positive quadratics has two roots;

If discriminant is negative quadratics has no root;

If discriminant is zero quadratics has one root.

When graphed quadratic expression (\(ax^2+bx+c=0\)) gives parabola:

The larger the absolute value of \(a\), the steeper (or thinner) the parabola is, since the value of y is increased more quickly.

If \(a\) is positive, the parabola opens upward, if negative, the parabola opens downward.

Viete's theorem

Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).

Common mistake to avoid Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

For example, \(xy=y\) cannot be reduced by \(y\) because \(y\) could be 0 and we cannot divide by 0. If we do we'll loose one of the solutions. The correct way is: \(xy=y\) --> \(xy-y=0\) --> \(y(x-1)=0\) --> \(y=0\) or \(x=1\).

Please share your Algebra tips below and get kudos point. Thank you.

hi man great you are ..

I want to know parabola... please let me understand few things as under:

1. When graphed quadratic expression (ax^2 + bx + c= 0) gives parabola: Perhaps, on the graph, you plotted a, b, and c, please say to me which one is which ...?

2. The larger the absolute value of a, the steeper (or thinner) the parabola is, since the value of y is increased more quickly: please shed some light on this concept ....

3. If a is positive, the parabola opens upward, if negative, the parabola opens downward. also, shed some light ...

maybe they are very obvious....but I need some sort of clarification and your help...

thanks in advance, man..

Last edited by gmatcracker2017 on 20 Sep 2017, 09:34, edited 1 time in total.

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

The general form of a quadratic equation is \(ax^2+bx+c=0\). It's roots are: \(x_1=\frac{-b-\sqrt{b^2-4ac}}{2a}\) and \(x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}\)

Expression \(b^2-4ac\) is called discriminant:

If discriminant is positive quadratics has two roots;

If discriminant is negative quadratics has no root;

If discriminant is zero quadratics has one root.

When graphed quadratic expression (\(ax^2+bx+c=0\)) gives parabola:

The larger the absolute value of \(a\), the steeper (or thinner) the parabola is, since the value of y is increased more quickly.

If \(a\) is positive, the parabola opens upward, if negative, the parabola opens downward.

Viete's theorem

Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).

Common mistake to avoid Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

For example, \(xy=y\) cannot be reduced by \(y\) because \(y\) could be 0 and we cannot divide by 0. If we do we'll loose one of the solutions. The correct way is: \(xy=y\) --> \(xy-y=0\) --> \(y(x-1)=0\) --> \(y=0\) or \(x=1\).

Please share your Algebra tips below and get kudos point. Thank you.

hi man great you are ..

I want to know parabola... please let me understand few things as under:

1. When graphed quadratic expression (ax^2 + bx + c= 0) gives parabola: Perhaps, on the graph, you presented a, b, and c, please say to me which one is which ...?

2. The larger the absolute value of a, the steeper (or thinner) the parabola is, since the value of y is increased more quickly: please shed some light on this concept ....

3. If a is positive, the parabola opens upward, if negative, the parabola opens downward. also, shed some light ...

maybe they are very obvious....but I need some sort of clarification...

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

The general form of a quadratic equation is \(ax^2+bx+c=0\). It's roots are: \(x_1=\frac{-b-\sqrt{b^2-4ac}}{2a}\) and \(x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}\)

Expression \(b^2-4ac\) is called discriminant:

If discriminant is positive quadratics has two roots;

If discriminant is negative quadratics has no root;

If discriminant is zero quadratics has one root.

When graphed quadratic expression (\(ax^2+bx+c=0\)) gives parabola:

The larger the absolute value of \(a\), the steeper (or thinner) the parabola is, since the value of y is increased more quickly.

If \(a\) is positive, the parabola opens upward, if negative, the parabola opens downward.

Viete's theorem

Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).

Common mistake to avoid Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

For example, \(xy=y\) cannot be reduced by \(y\) because \(y\) could be 0 and we cannot divide by 0. If we do we'll loose one of the solutions. The correct way is: \(xy=y\) --> \(xy-y=0\) --> \(y(x-1)=0\) --> \(y=0\) or \(x=1\).

Please share your Algebra tips below and get kudos point. Thank you.

hi man great you are ..

I want to know parabola... please let me understand few things as under:

1. When graphed quadratic expression (ax^2 + bx + c= 0) gives parabola: Perhaps, on the graph, you presented a, b, and c, please say to me which one is which ...?

2. The larger the absolute value of a, the steeper (or thinner) the parabola is, since the value of y is increased more quickly: please shed some light on this concept ....

3. If a is positive, the parabola opens upward, if negative, the parabola opens downward. also, shed some light ...

maybe they are very obvious....but I need some sort of clarification...

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