Question

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

Answer 1

Answer:

-$(x-4)^{2}$

or -$x^{2}$+8x-16

Step-by-step 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