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What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?

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What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?  [#permalink]

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New post 06 Mar 2018, 22:08
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A
B
C
D
E

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  15% (low)

Question Stats:

84% (00:34) correct 16% (00:46) wrong based on 51 sessions

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Re: What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?  [#permalink]

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New post 06 Mar 2018, 22:09
Bunuel wrote:
What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?

A. -3
B. 0
C. 3
D. 6
E. 9


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What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?  [#permalink]

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New post 06 Mar 2018, 22:49
Bunuel wrote:
What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?

A. -3
B. 0
C. 3
D. 6
E. 9


Factorizing the quadratic equation, we get
\(x^2 - 3x - 54 = x^2 - 9x + 6x - 54\) = 0 -> \(x(x-9) + 6(x-9) = 0\)

x could take the value 9 or -6, making the sum of the solutions, 9 - 6 = 3(Option C)

Alternate approach

The quadratic equation is of the form \(ax^2\) + bx + c = 0

the sum of the roots = -\(\frac{b}{a}\) and the product of the roots = \(\frac{c}{a}\)

Since the quadratic equation is \(x^2 - 3x - 54 = 0\), the sum of the roots is \(\frac{-(-3)}{1}\) = 3 (Option C)

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Re: What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?  [#permalink]

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New post 06 Mar 2018, 23:34
Bunuel wrote:
What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?

A. -3
B. 0
C. 3
D. 6
E. 9


For quadratic equation in the form of \(ax^2+bx+c = 0\), sum of roots is \(\frac{-b}{a}\)and product is \(\frac{c}{a}.\)

We are concerned with sum, so = \(\frac{-b}{a}\) = \(\frac{-(-3)}{1}\)\(= 3\)

Therefore, (C)
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Re: What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?  [#permalink]

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New post 08 Mar 2018, 17:59
Bunuel wrote:
What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?

A. -3
B. 0
C. 3
D. 6
E. 9


We can solve for x:

x^2 − 3x − 54 = 0

(x - 9)(x + 6) = 0

x = 9 or x = -6, so the sum is 3.

Answer: C
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Re: What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0?   [#permalink] 08 Mar 2018, 17:59
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