Question

verify that the numbers given alongside of the cubic polynomials below are thier zero also verify the relationship between the zeroes and the coefficients in each case. 2x³+x²-5x+2; ½, 1, -2​

Answer 1

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Answer 2

Thus, 1/2, 1 and -2 are the zeroes of the given polynomial.

Comparing the given polynomial with ax3 + bx2 + cx + d, we get a=2, b=1, c=-5, d=2

Also, α=1/2, β=1 and γ=-2

Now,

-b/a = α+β+γ

⇒ 1/2 = 1/2 + 1 - 2

⇒ 1/2 = 1/2

c/a = αβ+βγ+γα

⇒ -5/2 = (1/2 × 1) + (1 × -2) + (-2 × 1/2)

⇒ -5/2 = 1/2 - 2 - 1

⇒ -5/2 = -5/2

-d/a = αβγ

⇒ -2/2 = (1/2 × 1 × -2)

⇒ -1 = 1

Thus, the relationship between zeroes and the coefficients are verified.