Question

If x – 3 and x- 1/3
are both factors of px^2 + 5x + r , then show that P = r

Answer 1

As (x-3) and (x-1/3) are factors of this quadratic equation, it implies that 3 and 1/3 are zeroes of this equation

Implies, p(3^2) + 5(3) + r = 0

9p + 15 + r = 0

9p + r = 15. (1)

On substituting 1/3

p(1/3) ^2 + 5(1/3) + r = 0

p/9 + 5/3 + r = 0

p + 15 + 9r = 0

9

9r + p = -15. (2)

From eq 1 and 2 we can say that P=r

Therefore p=r . I hope this would help you.

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