Question

If y = -1 is a zero of the polynomial q(y) =4y³+ky²-y-1 then find the value of k. ​

Answer 1

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Answer 2

The value of k is 4, if y = -1 is a zero of the polynomial q(y) =4y³+ky²-y-1 .

Given:

• A polynomial $q(y) = 4 {y}^{3} + k {y}^{2} - y - 1$
• A zero of q(y) at y=-1.

To find:

• Find value of k.

Solution:

Concept to be used:

If x=a is a zero of polynomial p(x), then p(a)=0.

Step 1:

Put the value of y=-1 in the polynomial.

$q( - 1) = 4 {( - 1)}^{3} + k {( - 1)}^{2} -( - 1) - 1$

or

$q( - 1) = 4 {( - 1)} + k {( 1)} + 1- 1$

or

$\bf q( - 1) = - 4 + k$

Step 2:

Put q(-1)=0

$- 4 + k = 0$

or

$\bf k = 4$

Thus,

Value of k= 4, if y = -1 is a zero of the polynomial q(y) =4y³+ky²-y-1 .

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