The quadratic equation x^(2)+q=8x has equal roots. Find the value of q.

Question

The quadratic equation
`x^(2)`+q=8x has equal roots. Find the value of q.

Answer 1

q = 16

Explanation:

x^2 + q = 8x

Rearrange:

x^2 -8x + q = 0

We are told the equation has equal roots. Lets assign the letter z to that root.

Since the equation has equal roots, it can be factored: (x + z)*(x + z)

x^2 -8x + q = (x+z)(x+z)

x^2 -8x + q = (x^2 +2zx + z^2)

Therefore:

1) -8x = 2zx, and

2) q = z^2

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Solve the first for z:

1) -8x = 2zx,

-8 = 2z

z = -4

Since q = z^2,

q = (-4)^2 or 16

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CHECK:

Does x^2 + 16 = 8x have equal roots?

x^2 + 16 = 8x

x^2 - 8x + 16 = 0

(x - 4)(x - 4) YES