Question

if α and β are the roots of the quadratic equation x²-x-2=0 then α²+β² is equal to 1)5 2)2 3)9 4)-2

Answer 1

Answer:

ANSWER

f(x)=x

2

−2x+3 have zeroes α,β

⇒α+β=2

⇒α⋅β=3

Now polynomial having α+2,β+2 as roots is

p(x)=x

2

−(α+2+β+2)x+(α+2)(β+2)

=x

2

−(α+β+4)x+αβ+2(α+β)+4

=x

2

−(2+4)x+3+2(2)+4

⇒x

2

−6x+11

Please mark it

Answer 2

Hope it helps you see the attachment