Question

verify that 3,-2,1 are zeroes of the cubic polynomial p(x)=xcube -2xsquare+5x+6verify the relationship between the zeroes and its coefficient ​

Answer 1

Answer:

Step-by-step explanation:

Given,p(x)=x3-2x2+5x+6

Now,p(3)=xcube-2(3)square+5(3)+6

              =27-18+15+6

              =30 not equal to zero therefore 3 is not a zero of p(x)

Similarly,p(-2)=(-2)cube-2(-2)square+5(-2)+6

                       =4-8-10+6

                        = -8not equal to zero........p(x)

and,p(1)=1 cube-2(1)square+5(1)+6

             =1-2+5+6

              =10 not equal to zero .............p(x)

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Answer 2

3 , -2 , 1 are not the zeros of given polynomial

Solution:

Given polynomial equation is:

$p(x) = x^3 - 2x^2 + 5x + 6$

x = k , is a zero of polynomial f(x), if and only p(k) = 0

Substitute x = 3

$p(3) = 3^3 - 2(3)^2 + 5(3) + 6 \\\\p(3) = 27 - 18 + 15 + 6 \\\\p(3) = 30$

$p(3)\neq 0$

Thus, x = 3 is not a zero of given polynomial

Substitute x = -2

$p(-2) = (-2)^3 - 2(-2)^2 + 5(-2) + 6 \\\\p(-2) = - 8 - 8 - 10 + 6 \\\\p(-2) = -20\\\\p(-2) \neq 0$

Thus, x = -2 is not a zero of given polynomial

Substitute x = 1

$p(1) = 1^3 - 2(1)^2 + 5(1) + 6 \\\\p(1) = 1 - 2 + 5 + 6 \\\\p(1) = 10\\\\p(1) \neq 0$

Thus, x = 1 is not a zero of given polynomial

Learn more:

Verify that 1, 2 and 3/2are the zeroes of the cubic polynomial p (x) = 2x3 - 9x2 + 13x - 6.

Then, verify the relationship between the zeroes and the coefficients of the polynomial.​

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