Question

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Examine which of the numbers 1,-1,-3 are zeroes of the polynomial p(x) = 2x^4 + 9x^3 + = 11x^2 + 4x - 6

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Answer 1

Answer:

Let f(x)=2x⁴ +9x³ +11x²+4x−6.

p(1)=2(1)⁴ +9(1)³ +11(1)² +4(1)−6

=2+9+11+4−6

= 20

∴ 1 is not a zero of the polynomial p(x)

Again p(−1)=2(−1)⁴ +9(−1)³ +11(−1) ²+4(−1)−6

=2−9+11−4−6=−6

= -6

∴ −1 is not a zero of the polynomial f(x).

Also p(−3)=2(−3)⁴+9(−3)³ +11(−3)² +4(−3)−6

=162−243+99−12−6

= 0

∴ −3 is a zero of the polynomial f(x).

Thus 1 and −1 are not zeros of p(x), whereas −3 is zero of p(x)

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