Number of real roots of polynomial equation x^4-x^2+2 x-1=0 is

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

normal

The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is

A

$0$

B

$2$

C

$3$

D

$4$

(KVPY-2018)

Solution

(b)

Given,

$x^4-x^2+2 x-1=0$

$x^4-(x-1)^2=0$

$\left(x^2-x+1\right)\left(x^2+x-1\right)=0$

$x^2-x+1=0$ Or $x^2+x-1=0$

$x^2-x+1=0$ has no real roots.

$x^2+x-1=0$ has two real roots

Standard 11

Mathematics

Share

Similar Questions

For the equation $|{x^2}| + |x| – 6 = 0$, the roots are

hard

The solutions of the quadratic equation ${(3|x| – 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x – 3)} $ are given by

hard

The product of all real roots of the equation ${x^2} – |x| – \,6 = 0$ is

medium

If $a < 0$ then the inequality $a{x^2} – 2x + 4 > 0$ has the solution represented by

easy

Let $\alpha ,\beta $ be the roots of ${x^2} + (3 – \lambda )x – \lambda = 0.$ The value of $\lambda $ for which ${\alpha ^2} + {\beta ^2}$ is minimum, is

medium