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) = 4x^{2} + 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 4x^{2} + 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 4x^{2} + 3x – 1.

Hence, x = 1/4 and x = -1 are zeroes of the polynomial 4x^{2} + 3x – 1.

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