Question

17. If a and ß are the zeroes of the polynomial x ^ 2 + 7x + 12 then form a quadratic polynomial whose zeroes are 2a and 2ß.​

Answer 1

Step-by-step explanation:

Correct option is

C

16x2−9x+1

Given that α & β are zero of polynomial

f(x)=x2−3x−2

therefore α+β=3

αβ=−2

Now, the zero of the required quadratic polynomial are,

2α+β1 & 2β+α1

Sum of the roots-

2α+β1+2β+α1=(2α+β)(2β+α)2β+α+2α+β=4αβ+2α2+2β2+αβ3(α+β)

=4×(−2)+2[(α+β)2−2αβ]+(−2)3×3

=−10+2[9+2×2]9

=−10+269

=169

Products of roots:-

2α+β1