Question

Why are 1/4
and-1 zeroes of the polynomials p(x) = 4*2 + 3x – 1?​

Answer 1

Answer:

A zero or root of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero.

Therefore, if p(x)=0, for a given x then the value of x is zero of polynomial.

p(x) = 4x² + 3x – 1

For 1/4,

p(1/4) = 4(1/4)² + 3(1/4) – 1

⇒ p(1/4) = 1/4 + 3/4 – 1

⇒ p(1/4) = 1 – 1

⇒ p(1/4) = 0

Therefore, x = 1/4 is a zero of the

polynomial 4x² + 3x – 1.

For -1,

p(-1) = 4(-1)² + 3(-1) – 1

⇒ p(-1) = 4 – 3 – 1

⇒ p(-1) = 4 – 4

⇒ p(-1) = 0

Therefore, x = -1 is a zero of the

polynomial 4x² + 3x – 1.

Hence, x = 1/4 and x = -1 are zeroes of the polynomial 4x² + 3x – 1.