Question

Write an equation in standard form with zeros 2 and -8

Answer 1

Standard form of polynomial with zeros 2 and -8 is
`P(x) = x^2 + 6x - 16`

Explanation:

Here, the zeroes of the polynomial P(x) is given as x = 2 and x = -3

If x = a is a zero pf the polynomial p(x) , then (x-a) is the root of the given polynomial.

⇒ (x- 2) and (x -(-8)) are the two roots of the polynomial P(x).

Now, Polynomial P(x) = Product of all its Roots

`⇒P(x)  =  (x- 2) (x +8 )\\= x(x+8) -2(x+8)  = x^2 + 8x - 2x- 16\\= x^2 + 6x - 16 \\\implies P(x) = x^2 + 6x - 16`

Hence the standard form of polynomial with zeros 2 and -8 is
`P(x) = x^2 + 6x - 16`