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# A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum

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Senior RC Moderator
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A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum [#permalink]

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14 Jul 2017, 07:34
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A given quadratic equation $$ax^2 – 52x + 24 = 0$$ has $$\frac{13}{6}$$ as sum of the roots. Find the product of the roots.

(A) $$24$$
(B) $$1$$
(C) $$12$$
(D) $$\frac{24}{5}$$
(E) $$2$$
[Reveal] Spoiler: OA

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Re: A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum [#permalink]

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14 Jul 2017, 08:09
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Let the roots of the equation be x and y

Now sum of the roots = x+y = - (-52)/a

Product of the roots = x*y = 24/a

Given sum of the roots = 13/6 = 52/a => a = 52*6/13

Product of the roots = x*y = 24/a = (24 * 13)/(52 * 6) = 1

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Re: A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum [#permalink]

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14 Jul 2017, 08:57
Sum of the roots of a quadratic equation $$= \frac{b}{a} = \frac{-(-52)}{a} = \frac{13}{6}$$, hence, $$a = 24.$$

Product of the roots $$= \frac{c}{a} = \frac{24}{24} = 1.$$ Ans - B.
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Re: A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum [#permalink]

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01 Aug 2017, 08:22
TimeTraveller wrote:
Sum of the roots of a quadratic equation $$= \frac{b}{a} = \frac{-(-52)}{a} = \frac{13}{6}$$, hence, $$a = 24.$$

Product of the roots $$= \frac{c}{a} = \frac{24}{24} = 1.$$ Ans - B.

Hi,
I can't understand why you put a minus in front of -54; can you please clarify?

Thanks a lot,
MvArrow
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Re: A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum [#permalink]

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02 Aug 2017, 10:04
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In a quadratic equation "ax^2+bx+c"

Sum of roots = -b/a
&
Product of roots = c/a

Hope this helps u.
Re: A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum   [#permalink] 02 Aug 2017, 10:04
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# A given quadratic equation ax2 – 52x + 24 = 0 has 13/6 as sum

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