Question

If a and B are the zeroes of the
polynomial 21x² -x - 2, find a
quadratic polynomial whose zeroes are 2a and 2B.​

Answer 1

Given:-

Zeroes of polynomial p(x) = 21x^2-x-2=0 is a and b

Here,

21x^2-x-2=0

=>21x^2-(7-6)x-2=0

=>21x^2-7x+6x-2=0

=>7x(3x-1)+2(3x-1)=0

=>{3x-1)(7x+2)=0

Now,

3x-1=0 ; 7x+2=0

=>3x=1 ; =>7x=-2

Therefore, x=1/3 ; x=-2/7

Before we considered that x=a ; x=b

So,

a=1/3 ; b=-2/7

Now,

2a=2{1/3) ;2b2(-2/7)

Hence, 2a=2/3 ; 2b=-4/7

I HOPE THAT IT HELPS YOU.