Question

alpha and beta are the zeroes of a quadratic polynomial ax2 + bx + c then evaluate 1/alpha + 1/beta-2 alpha beta

Answer 1

Hi friend!!!

Given, alpha and beta are the zeroes of a quadratic polynomial ax2 + bx + c

œ+ß=-b/a

ϧ=c/a

1 /œ+1/ß-2œß

=(œ+ß) /œß-2œß

=-b/a/c/a-2c/a

=-b/c-2c/a

=-ba-2c²/ac


I hope this will help u ;)

Answer 2

Hey !!

p(x) = ax² + bx + c

α and β are zeros of p(x)

α + β = -b/a
αβ = c/a

to find :-

1/α + 1/β - 2αβ

[α + β]/αβ - 2αβ

$\frac{ \frac{-b}{a} }{ \frac{c}{a} }$ - 2 × c/a
 = -b/c - 2c/a
 = -ba - 2c²/ac