Question

If α and β are the zeroes of a polynomial x² - x-30, then form a quadratic Polynomial whose zeroes are 2-α and 2- β

Answer 1

As α and β are

the zeroes of polynomial x²-x-30,

we can say,

α+β=-b/a=1 ------------(i)and,

αβ=c/a=-30 ---------(ii)

Then, a quadratic polynomial whose zeroes are (2-α) and (2-β) is

f(x)= x²- (2-α+2-β)x + (2-α)(2-β)

=x²-{4-(α+β)}x+{4-2(α+β)+αβ}

Putting the values from (i) and (ii),

=x²-(4-1)x+(4-2-30)

=x²-3x-28(Ans.)

hope this help u