Question

Find the value of k such that the quadratic polynomials x2-(k+6)x+2(2k+1) as sum of the zeroes as the half of their product

Answer 1

k = 5

Explanation:

The sum of the zeros is the opposite of the coefficient of x, so is (k+6).

The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).

The problem statement asks us to find k so that these values are the same:

k +6 = 2k +1

5 = k . . . . . . . . subtract k+1

The value of k is 5.

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The zeros are 5.5±√8.25. Their sum is 11; their product is 22.