Question

if alpha + beta are zeros of the quadratic polynomial f(x)=x2+x-2,find the values of 1/alfa-1/beta​

Answer 1

Step-by-step explanation:

We have,px = x2-x-2

Since α and βare zeroes of px, thenα+β = -coefficient of xcoefficient of x2= 1α×β = constant termcoefficient of x2 = -2

Now,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 = 4

Product of zeroes of required polynomial = P⇒P = 2α+1 × 2β+1 = 4αβ + 2α+β + 1 = 4-2 + 21 + 1 = -8 + 3 = -5

Now required polynomial is,fx = kx2 - Sx + P, k is a non zero real number = kx2-4x-5Taking k = 1, we get fx = x2-4x-5

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