α and β are the zeros of a polynomial, such that α+β=6 and αβ=4. Identify the polynomial. A x 2 −6x+4 B a 2 +6a+4 C p 2 +6p−4 D m 2 −6m−4

Question

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

A

x2−6x+4

B

a2+6a+4

C

p2+6p−4

D

m2−6m−4

Easy

Solution

Verified by  GMS

Correct option is A)

Let 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=a−b​

Product of the roots =α×β=ac​

We can also write p(x) in this form also 

p(x)=x2−a−b​x+ac​

 
⇒p(x)=x2−(α+β)x+αβ 

Now given that α+β=6 and αβ=4

Substituting these values we get

p(x)=x2

$-(6)x+4$ is the required polynomial.