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Question

# α and β are the zeros of a polynomial, such that α+β=6 and αβ=4. Identify the polynomial.

A
x26x+4
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B
a2+6a+4
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C
p2+6p4
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D
m26m4
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Solution

## The correct option is A x2−6x+4Let p(x)=ax2+bx+c where a≠0 is a quadratic polynomial α,β are the zeroes of p(x)We know that Sum of the roots =α+β=−ba Product of the roots =α×β=ca We can also write p(x) in this form also p(x)=x2−−bax+ca ⇒p(x)=x2−(α+β)x+αβ Now given that α+β=6 and αβ=4Substituting these values we getp(x)=x2−(6)x+4 is the required polynomial.

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