Question

alpha and beta are 0s of a quadratic polynomial x^2-x-30 the form of a quadratic polynomial whose 0s are 2-alpha and 2-beta

Answer 1

hey mate

here is the answer....

Answer:

@ and b are two zeros!

on factorising, x²-x-30

=>x²-x-30=0

=>x²-(6-5)x+30=0

=>x²-6x+5x-30=0

=>x(x-6)+5(x-6)=0

=>(x-6)(x+5)=0

=>x=6 and -5

thus,

=>2-@=2-(-5)

=>2+5=7

--------+++++++----------

=>2-b=2-(6)

=>-4

hence the quadratic polynomial with roots 7 and -4 are

x²-(sum of the roots)x+(product of the roots)

=>x²-(7-4)x+(7*-4)

=>x²-3x+28 (Answer)

Answer 2

Answer:

P(x)=x²-x-30

α+β=1

αβ=-30

Zeros:2-α,2-β

α+β=2-α+2-β

=4-(α+β)

=4-1=3

αβ=(2-α)(2-β)

=4-2α-2β+αβ

=4-2(α+β)+αβ

=4-2(1)+(-30)

=4-2-30

=-28

Q.poly= x²-3x+28

Hope it helps u.....^_^