Verify whether $- 3$ and $2$ are the zeroes of the polynomial $x^{3} - x^{2} + x - 6$ .

Open in App

Solution

We know, if $a$ is a zero of $f (x)$ , then $f (a) = 0$ .

Given, $f (x) = x^{3} - x^{2} + x - 6$ .

Let $x = - 3$ :
Then $f (- 3) = (- 3)^{3} - (- 3)^{2} + (- 3) - 6 = - 27 - 9 - 3 - 6 = - 45 \neq 0$ .
That is, $x = - 3$ is not a zero of the given polynomial $f (x)$ .

Now let $x = 2$ :
Then $f (2) = (2)^{3} - (2)^{2} + (2) - 6 = 8 - 4 + 2 - 6 = 0$ .
That is, $x = 2$ is a zero of the given polynomial $f (x)$ .

Hence, $x = 2$ is a zero of the given polynomial $f (x)$ but $x = - 3$ is not.

Suggest Corrections

Similar questions

Q. Verify whether

2

and

3

the zeroes of the polynomial

x^{2} - 5 x + 6

Q. Verify that

1, - 1,

and

- 3

are the zeroes of the cubic polynomial,

x^{3} + x^{2} - x - 3

and verify the relationship between zeroes and the coefficients.

Q. Verify whether

2

and

1

are zeroes of the polynomial

x^{2} - 3 x + 2

Verify that
(i) 1 and 2 are the zeros of the polynomial, $p (x) = x^{2} - 3 x + 2$ .
(ii) 2 and -3 are the zeros of the polynomial, $q (x) = x^{2} + x - 6.$
(iii) 0 and 3 are the zeros of the polynomial, $r (x) = x^{2} - 3 x$ .

Q. Verify that 3, -2, 1 are the zeroes of the cubic polynomial

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

Join BYJU'S Learning Program

Verify whether −3 and 2 are the zeroes of the polynomial x3−x2+x−6.

Verify whether $- 3$ and $2$ are the zeroes of the polynomial $x^{3} - x^{2} + x - 6$ .