Question

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2?

Answer 1

The correct answer is D, or
`f(x) = -x^2 + 8x - 16`

Just got it right on Edge 2020, hope this helps!! :)

Answer 2

-
`(x-4)^(2)`

or -
`x^(2)`+8x-16

Explanation:

Given a second degree polynomial has a root 4 with multiplicity 2

That means, 4 is a repeating root of the polynomial.

Any second degree polynomial has at most 2 real roots.

⇒Both roots of the polynomial are 4.

and its expression can be written as c·
`(x-4)^(2)` where c is a real number

⇒c·(
`x^(2)`-8x+16)

⇒c
`x^(2)`-8cx+16c

Also, the leading coefficient is given as -1

So, c = -1

and the expression becomes (-1)
`x^(2)`-8·(-1)·x+16·(-1)

⇒-
`x^(2)`+8x-16