Problem Solving

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

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.