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

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0? [#permalink]

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06 Mar 2018, 22:08
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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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
Re: What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0? [#permalink]

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06 Mar 2018, 22:09
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Joined: 26 Feb 2016
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What is the sum of the solutions to the quadratic x^2 − 3x − 54 = 0? [#permalink]

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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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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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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.

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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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