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Question

if alpha and bita are zeroes of the quadratic polynomial ax2+bx+c,then find a quadratic polynomial whose zeroes are

1/alpha and 1/bita.

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Solution

The given polynomial is,px = ax2 + bx + cSince α & β are zeroes of px, thenα + β = -baα × β = caNow, 1α and 1β are the zeroes of required polynomialSum of zeroes of required polynomial, S = 1α + 1β = β + ααβ = -baca = -bcProduct of zeroes of required polynomial, P = 1α × 1β = 1αβ = ac

Hence, required polynomial is,fx = kx2 - Sx + P, k is non zero real number = k x2 + bcx + ac = kc cx2 + bx + aTaking k = c, we get,fx = cx2 + bx + a

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