Question

if a and b are zeros of polynomialf(x)=x2-3x-2,find the quadratic polynomial whose zeros are 1/2a+b and 1/2b+a

Answer 1

Answer: 16x^2-9x+1

Step-by-step explanation:

Just read the steps carefully and I’m sure you will be able to do this question easily:)

Hope it helps!

Answer 2

Answer:

x^2-(α+β)x+αβ

Step-by-step explanation:

the given polynomial is x^2-3x-2

zeros = α,β

sum of zeros= -b/a

α+β=3

product of zeros= c/a

αβ = 3

sum of squares of zeros=

ac+(αβ)^2 = 3^2

a^2+20β+β^2=9

α^2+β^2=9+2αβ

α^2+β^2=13

now the polynomial is

x^2-(α+β)x+αβ