Question

if alpha and beta are the zeros of the quadratic polynomial FX = X square + X - 2 find the value of one by Alpha minus one by beta

Answer 1

Since , FX is a quadratic polynomial
and standard form of quadratic equation is
x^2 - (alpha + beta)x + (alpha × beta )
On comparing given equation ,
alpha + beta = -1
alpha × beta = -2
(alpha + beta)^2 -4(alpha × beta) = (alpha - beta)^2
(-1)^2 -4×(-2) = (alpha - beta)^2
1 + 8 = 9 = (alpha - beta)^2
(alpha - beta) = 3 , eq(1)
1/alpha - 1/beta = (beta - alpha) / (alpha × beta)
= -3 / -2 = 3/2