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# Math- Equation solving for k?

Find the values of k for which the equation x^2 + k + 6 = kx +3x has equal roots

### 2 Answers

- Random StrangerLv 68 years agoFavorite Answer
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x^2 + k + 6 = kx +3x

x^2 -x(k+3) + (k+6) = 0

The equation will have equal roots only if the polynomial is a perfect square. That happens when the discriminant is zero. So, solve

(k+3)^2 - 4(k +6) = 0

k^2 + 6k + 9 - 4k - 24 = 0

k^2 + 2k - 15 = 0

(k+5)(k-3) = 0

k = -5 or k = 3 <--- answer

==

Check

When k = -5

x^2 - x(-5 + 3) + (-5 + 6) = 0

x^2 -2x + 1 = 0

(x-1)^2 = 0 <--- equal roots

When k = 3

x^ - x(3+3) + (3+6) = 0

x -6x + 9 = 0

(x-3)^2 = 0 <--- equal roots

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