Question

If alpha and beta are the zeros of the quadratic polynomial x2 + x - 2, find the value of 1/alpha - 1/beta

Answer 1

hey there,

"If alpha and beta are the zeroes of the polynomial"

Taking this into account

1/alpha - 1/beta = 1/0 - 1/0
= infinity - infinity
which is not defined

if incase
"If alpha and beta are the solutions of the polynomial"

x^2 + x - 2 =0

(x+2)(x -1) = 0

=> x= -2 or x =1

therefore (alpha,beta) = (1,-2) or (-2,1)

1/alpha - 1/beta = +(3/2) or -(3/2)

Hope this helps!

Answer 2

We have,px = x2-x-2Since α and βare zeroes of px, thenα+β = -coefficient of xcoefficient of x2= 1α×β = constant termcoefficient of x2 = -2Now,2α+1 and 2β+1 are the zeroes of required polynomial.Sum of zeroes of required polynomial = S⇒S = 2α+1 + 2β+1 = 2α+β + 2 = 2+ 2 = 4Product of zeroes of required polynomial = P⇒P = 2α+1 × 2β+1 = 4αβ + 2α+β + 1 = 4-2 + 21 + 1 = -8 + 3 = -5Now required polynomial is,fx = kx2 - Sx + P, k is a non zero real number = kx2-4x-5Taking k = 1, we getfx = x2-4x-5