Question

Verify whether the indicated numbers are zeroes of their corresponding polynomials.

(a) Q(s) = -4s3 + 7s2 - 24; s = -4 and 1

(b) 8t sq + 4t - 4 ; t = 1/2 and -1


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Answer 1

Given,

Verify whether the indicated numbers are zeroes of their corresponding polynomials.

(a) Q(s) = -4s³ + 7s² - 24; s = -4 and 1

(b) 8t² + 4t - 4 ; t = 1/2 and -1

we know, if x = a is a zero of a polynomial g(x) then g(a) must be equal to zero. i.e, g(a) = 0.

(a) Q(s) = -4s³ + 7s² - 24

s = -4

Q(-4) = -4(-4)³ + 7(-4)² - 24

= 256 + 112 - 24 ≠ 0

so, -4 is not a zero of polynomial Q(s).

now s = 1

Q(1) = -4(1)³ + 7(1)² - 24 = -4 + 7 - 24 ≠ 0

so, 1 is also not a zero of polynomial Q(s).

(b) P(t) = 8t² + 4t - 4

t = 1/2

P(1/2) = 8(1/2)² + 4(1/2) - 4

= 8 × 1/4 + 2 - 4

= 2 + 2 - 4 = 0

here P(1/2) = 0 so 1/2 is a zero of given polynomial 8t² + 4t - 4.

again, t = -1

P(-1) = 8(-1)² + 4(-1) - 4

= 8 - 4 - 4

= 8 - 8 = 0

here P(-1) = 0 so -1 is also a zero of polynomial P(t) = 8t² + 4t - 4.

Answer 2

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