MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Definition of Functions

If -1 is a ...

Question

If $- 1$ is a zero of the polynomial $p (x) = a x^{3} - x^{2} + x + 4$ , find the value of $a .$

Open in App

Solution

$p (- 1) = a (- 1)^{3} - (- 1)^{2} - 1 + 4 = 0 \Rightarrow - a = - 2 \Rightarrow a = 2$

Suggest Corrections

thumbs-up

2

Similar questions

Q. Verify that:
(i) 4 is a zero of the polynomial p(x) = x − 4.
(ii) −3 is a zero of the polynomial p(x) = x − 3.
(iii)

- \frac{1}{2}

is a zero of the polynomial p(y) = 2y + 1.
(iv)

\frac{2}{5}

is a zero of the polynomial p(x) = 2 − 5x.
(v) 1 and 2 are the zeros of the polynomial p(x) = (x − 1)(x − 2).
(vi) 0 and 3 are the zeros of the polynomial p(x) = x² − 3x.
(vii) 2 and −3 are the zeros of the polynomial p(x) = x² + x − 6.

(x + 3)

(x^{2} + 5 x + 7)

are factors of the polynomial

P (x) = a x^{3} + b x^{2} + c x + d

a

.

α, β

are zeroes of the polynomial

p (x) = x^{2} - x - 4

, then find the value of

\frac{α}{β} + \frac{β}{α} + 3 (\frac{1}{α} + \frac{1}{β}) - 2 α β

Q. If one zero of the quadratic polynomial

x^{2} + p x + 4

is 2, the other zero is

α

. Find the value of

- p α

If x = - $\frac{1}{2}$ is a zero of the polynomial p(x)

= $8 x^{3} - a x^{2}$ - x + 2, find the value of a.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Definition of Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definition of Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon