Question

find zeroes of quadratic polynomial
2x2-10
and verify
the relationship between
the zeroes and the coefficients

Answer 1

p(x) = 2x²-10 = 2(x²-5) =2[(x)²-(√5)²] = 2(x+√5)(x-√5)

let p(x) = 0

then,. 2(x+√5)(x-√5)= 0

=> (x+√5)=0 & (x-√5)=0

=> (x= -√5) & (x= √5)

So, -√5 & √5 are the zeroes of p(x).

Now,. let α = √5 & β = -√5.

α+β = -√5+√5 = 0 = -coefficient of x/coefficient of x²

αβ = -√5 × √5 = -5 = -10/2 = constant term/coefficient of x²