Question

If alpha and beta are zero of x^2+x-2 find 1/alpha-1/beta

Answer 1

Answer:

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

Answer 2

Answer:

$1 \div \alpha - 1 \div \beta = - 1 \div - 2 = 1 \div 2$