Question

If both (x-2) and (x-1/2) are factors of pz^2 + 5x + r , show that p=r

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Answer 1

g(x) = px² + 5x + r

Factors = (x - 2) , (x - 1/2)

∴ zeroes = 2 , 1/2

☛ Product of zeroes = (constant term) / (coefficient of x²)

☛ 2 × 1/2 = r/p

☛ 1 = r/p

☛ p = r

Hence, Proved.