Question

if a and b are the zeroes of quadratic polynomial x2-x-30,then form a quadratic polynomial whose zeroes are 2-a and 2-b

Answer 1

Let p(x) represent the above polynomial.

p(x)=x²-x-30

Given that a and b are the zeros of the polynomial.

=x²+5x-6x-30

=(x+5)(x-6)

We know that,

p(x)=0

→(x+5)(x-6)=0

→x=6 or x= -5

→a=6 and b= -5

Finding the values of,

2-a=2-6= -4

and, 2-b=2-(-5)=2+5=7

Now,

x²-(Sum of zeros)x+Product of zeros

=x²-(-4+7)x+(7)(-4)

=x²-3x-28

Hence,x²-3x-28 is the required polynomial