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If the curve described by the equation y = x2 + bx + c cuts the x-axis

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If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 10:08
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If the curve described by the equation \(y = x^2 + bx + c\) cuts the \(x\)-axis at \(-4\) and \(y\) axis at \(4\), at which other point does it cut the \(x\)-axis?

A. -1
B. 4
C. 1
D. -4
E. 0

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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 10:49
+1 for A? I plugged in the other points to come up with an equation...not sure if I went about it the right way
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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 22:08
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SajjadAhmad wrote:
If the curve described by the equation y = x^2 + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

A. -1
B. 4
C. 1
D. -4
E. 0


Given, \(y = x^2 + bx + c\), cuts the x-axis at two points. One intersection point with x-axis is given. We need to find out the other point of intersection. In other words, 1 root of the quadratic equation is given, what is the value if the other root?

a) At (-4,0), \(0=(-4)^2+b*(-4)+c\) Or, 4b-c=16
b) At (0,4), \(4=0^2+b*0+c\) Or, c=4
So, 4b-4=16 Or, b=5.
Now, we have the equation of the curve, \(y=x^2+5x+4\), which has the roots: -4 and -1.
So, other other root is -1.

Ans. (A)
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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 02 Jan 2019, 09:53
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If the curve described by the equation y = x^2 + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

A -1
B 4
C 1
D -4
E 0

y = x^2 + bx + c is a quadratic equation and the equation represents a parabola.
The curve cuts the y axis at 4.
The x coordinate of the point where it cuts the y axis = 0.
Therefore, (0, 4) is a point on the curve and will satisfy the equation.
4 = 0^2 + b(0) + c
Or c = 4.

The product of the roots of a quadratic equation is c/a
In this question, the product of the roots = 4/1 = 4.

The roots of the quadratic equation are the points where the curve cuts the x-axis.
The question states that one of the points where the curve cuts the x-axis is -4.
So, -4 is one of roots.
Let r2 be the second root of the quadratic equation.
So, -4 * r2 = 4
or r2 = -1.

The second root is the second point where the curve cuts the x-axis, which is -1.




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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 02 Jan 2019, 10:34
When x=-4 y=0
so 16 -4b +c=0
When x=0, y = 4
so c=4
16-4b+c=20-4b=0
b= 5

the equation can be written as y=(x+4)(x+1)

y is equal to zero when x=-1 (Answer A)
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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 03 Jan 2019, 02:15
cfc198 wrote:
If the curve described by the equation y = x^2 + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

A -1
B 4
C 1
D -4
E 0

y = x^2 + bx + c is a quadratic equation and the equation represents a parabola.
The curve cuts the y axis at 4.
The x coordinate of the point where it cuts the y axis = 0.
Therefore, (0, 4) is a point on the curve and will satisfy the equation.
4 = 0^2 + b(0) + c
Or c = 4.

The product of the roots of a quadratic equation is c/a
In this question, the product of the roots = 4/1 = 4.

The roots of the quadratic equation are the points where the curve cuts the x-axis.
The question states that one of the points where the curve cuts the x-axis is -4.
So, -4 is one of roots.
Let r2 be the second root of the quadratic equation.
So, -4 * r2 = 4
or r2 = -1.

The second root is the second point where the curve cuts the x-axis, which is -1.




If you liked the question and explanation, please do hit the kudos button :)

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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis   [#permalink] 22 Feb 2020, 15:03
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