Question

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

Answer 1

Answer:

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

Step-by-step 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$P(x) = x^2 + 6x - 16$