Answer:
(c) 8x^2 -32x +32, repeated root is x=2.
Explanation:
A quadratic with repeated roots will be a multiple of a perfect square trinomial. The form of it will be ...
a(x -b)² = ax² -2abx +ab² = a(x² -2bx +b²)
Dividing by the leading coefficient will leave a monic quadratic whose constant is a (positive) perfect square, and whose linear term has a coefficient that is double the root of the constant.
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-x^2 + 18x + 81
Dividing by the leading coefficient gives ...
x^2 -18x -81 . . . . . a negative constant
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3x^2 - 6x + 9
Dividing by the leading coefficient gives ...
x^2 -2x +3 . . . . . . constant is not a perfect square
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8x^2 - 32x + 32
Dividing by the leading coefficient gives ...
x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2
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25x^2 - 30x - 9
Dividing by the leading coefficient gives ...
x^2 -1.2x -0.36 . . . . . . a negative constant
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x^2 - 14x + 196
The x-coefficient is not 2 times the root of the constant.
14 = √196 ≠ 2√196