Find the zeros of $p(x)=x^{3}-4 x$ and show them graphically.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Here,$p(x)=x^{3}-4 x$
$=x(x^{2}-4)$
$=x(x-2)(x+2)$
To find the zeros of $p(x)$,consider $p(x)=0$.
$\therefore x(x-2)(x+2)=0$
$\therefore x=0, x=2$ or $x=-2$.
$\therefore 0, 2$ and $-2$ are the zeros of $p(x)$.
To draw the graph of this polynomial,we take some different values of $x$ and prepare the following table:
$x$$-2$$-1$$0$$1$$2$
$p(x)=x^3-4x$$0$$3$$0$$-3$$0$

Plot these points as shown in the graph. We can see that this graph intersects the $X$-axis at three distinct points $(-2, 0)$,$(0, 0)$ and $(2, 0)$. Their $X$-coordinates are the zeros of this polynomial. So,the zeros of $p(x)$ are $-2, 0$ and $2$.

Explore More

Similar Questions

The zeros of $p(x) = 2 + x - x^{2}$ are.......

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

The zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ where $a \neq 0$ and $a, b, c, d \in R$ are $\alpha, \beta,$ and $\gamma$. Then $\alpha \beta \gamma = \dots$

Draw the graph of $p(x) = x^{2} + x - 12$ and find the zeros of this polynomial.

The graph of a linear polynomial is a $\ldots \ldots \ldots . . . .$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo