Question

Write a polynomial function whose zeros are {-2,-4,1}. (type
without space, start with f(x)=).

need answer with solutions please will be appreciated​

Answer 1

Answer :-

By using factor theorem :-

If -2 is a zero of a polynomial, then ( x + 2 ) will be factor of polynomial.

Similarly, If -4 is zero, then ( x + 4 ) will be factor of polynomial.

Also, If 1 is factor, then ( x - 1 ) will be factor of polynomial.

Hence,

⇒ p(x) = ( x + 2 ) ( x + 4 ) ( x - 1 )

⇒ p(x) = [ x (x + 2) + 4 (x + 2) ] ( x - 1 )

⇒ p(x) = [ x² + 2x + 4x + 8 ] ( x - 1 )

⇒ p(x) = [ x² + 6x + 8 ] ( x - 1 )

⇒ p(x) = x ( x² + 6x + 8 ) - 1 ( x² + 6x + 8 )

⇒ p(x) = x³ + 6x² + 8x - x² - 6x - 8

⇒ p(x) = x³ + 5x² + 2x - 8

Polynomial = x³ + 5x² + 2x - 8