Question

Solve :- $x^4-11x^2+28=0$

Short answer

Solution for equation will be -

$x=+\sqrt{7}$

$x=-\sqrt{7}$

$x=+2$

$x=-2$

Step-by-step solution

Step 1.  Given Data

Quadratic Equation =$x^4-11x^2+28=0$

Step 2.  To Find

We have to solve it and find the value of x.

Step 3.  Explanation

Let the value of $x^2=u$

Then the equation is -

${\left(x^2\right)}^2-11x^2+28=0$

Put the value of $x^2=u$

$u^2-11u+28=0$

$(u-7)(u-4)=0$

By using Zero product property -

$$\begin{gathered} u-7=0,u-4=0 \\ u=7,u=4 \end{gathered}$$

Step 4.  Calculation

Replace u with $x^2$

$x^2=7$, $x^2=4$

localid="1644920295156" $x=\pm \sqrt{7}$, $x=\pm \sqrt{4}$

$x=\pm \sqrt{7}$, $x=\pm 2$

There are four solutions -

• $x=+\sqrt{7}$
• $x=-\sqrt{7}$
• $x=-2$
• $x=+2$