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If sum of the roots of the equation x^2-5x+6 = 0 is a

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If sum of the roots of the equation x^2-5x+6 = 0 is a  [#permalink]

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New post 11 Feb 2018, 05:48
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If sum of the roots of the equation \(x^2 -5x+6 = 0\) is \(a\) and product fo the roots of the same equation is \(b\) then find \(a^b\)

A) \(1\)
B) \(5^6\)
C) \(6^5\)
D) \(30\)
E) \(11\)

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If sum of the roots of the equation x^2-5x+6 = 0 is a  [#permalink]

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New post 11 Feb 2018, 05:52
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GMATinsight wrote:
If sum of the roots of the equation \(x^2 -5x+6 = 0\) is \(a\) and product fo the roots of the same equation is \(b\) then find \(a^b\)

A) \(1\)
B) \(5^6\)
C) \(6^5\)
D) \(30\)
E) \(11\)

SOURCE: http://WWW.GMATINSIGHT.COM


Sum of roots \(=-(\frac{-5}{1})=5=a\)

Product of roots \(=\frac{6}{1}=6=b\)

therefore \(a^b=5^6\)

Option B
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Re: If sum of the roots of the equation x^2-5x+6 = 0 is a  [#permalink]

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New post 11 Feb 2018, 21:42
x^2 - 5x + 6 = 0
(x - 3)(x - 2) = 0

Hence the roots are x = 3 and x = 2.
The problem states that the sum of the roots is equal to A. Hence A = 3 + 2 = 5.
The problem also states that the product of the roots is equal to B. Hence B = 3*2 = 6

The problem is looking for A^B. Hence, the answer is 5^6 (option B).
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Re: If sum of the roots of the equation x^2-5x+6 = 0 is a  [#permalink]

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New post 24 Feb 2018, 22:59
sum of the roots formula is -b/a = -(-5)/1=5
in problem its is given as a soo a=5
product of roots is given as b
where its formula is c/a=6/1=6
b=6
a*b=5*6

option B
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Re: If sum of the roots of the equation x^2-5x+6 = 0 is a  [#permalink]

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New post 25 Feb 2018, 12:04
Very simple one.
x^2 - (sum of squares)x+(product of squares) = 0

Hence 5^6 = B
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Re: If sum of the roots of the equation x^2-5x+6 = 0 is a   [#permalink] 25 Feb 2018, 12:04
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