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2 years ago

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?

Mathematics

1 answer:

pychu [463]2 years ago

6 0

Answer:

Step-by-step 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.

Dividing by the leading coefficient gives ...

x^2 -18x -81 . . . . . a negative constant

Dividing by the leading coefficient gives ...

x^2 -2x +3 . . . . . . constant is not a perfect square

Dividing by the leading coefficient gives ...

x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2

Dividing by the leading coefficient gives ...

x^2 -1.2x -0.36 . . . . . . a negative constant

The x-coefficient is not 2 times the root of the constant.

14 = √196 ≠ 2√196

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