Math CentralQuandaries & Queries


Question from Jess, a student:

Find the value of a positive integer k such that f(x)=x^2 - 2kx + 55 has roots at k +3 and k - 3.

Hi Jess,

If a quadratic polynomial ax2 + bx + c has roots r and s then the sum of the roots is -b/a and the product of the roots is c/a. In your problem a = 1, b = -2k, c = 55, r = k + 3 and s = k - 3. Thus for the sum of the roots

r + s = -b/a so
k + 3 + k - 3 = -(-2k/1)

This doesn't give us any new information it just says 2k = 2k.

What equation is generated by the result for the product of the roots? Does it allow you to solve for k? Make sure you check your answer.



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