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

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

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

by GMATinsight » Sun Feb 11, 2018 4:48 am

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: https://WWW.GMATINSIGHT.COM

Answer: option B

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Source: Beat The GMAT — Problem Solving | Sun Feb 11, 2018 4:48 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

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

by EconomistGMATTutor » Sun Feb 11, 2018 11:40 am

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: https://WWW.GMATINSIGHT.COM

Answer: option B

Hi GMATinsight,
Let's take a look at your question.

The quadratic equation given is:
$$x^2-5x+6=0$$

We know that, for a quadratic equation ax^2+bx+c=0,
Sum of roots = -b/a
Product of roots = c/a

We can find the sum and product of roots of given quadratic equation as:
$$Sum\ of\ roots=a=-\frac{\left(-5\right)}{1}=5$$
$$Product\ of\ roots=b=\frac{6}{1}=6$$
$$a^b=5^6$$

Therefore, option B is correct.

Hope it helps.
I am available if you'd like any follow up.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Tue Feb 13, 2018 5:37 pm

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

In any quadratic equation of the form ax^2 + bx + c = 0, the sum of the two roots is -b/a and the product of the two roots is c/a. Thus here the sum of the two roots is -(-5)/1 = 5 and the product of the two roots is 6/1 = 6. Thus, a^b = 5^6.

Alternate Solution:

We solve x^2 -5x+6 = 0 by factoring:

(x - 3)(x - 2) = 0

So, x = 3 and x = 2 are the roots. Thus, a = 3 + 2 = 5, and b = 3 x 2 = 6. We see, then, that a^b = 5^6.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]