Question

if alpha and beta are zeroes of a quadratic polynomial x^2 - x - 30, then form a quadratic polynomial whose zeros are 2 - alpha and 2 - beta

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.)

Answer 2

Answer:

Step-by-step explanation:

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.)