Name: Roots of Quadratic Equation: Illustration
Uploaded: 2019-07-19
Duration: 5 min 27 s
Description: Mixing certain chemicals can result in an explosion. Similarly, when we introduce new quadratic variables, it may lead to destruction or may become easier to...

Question

Solve the following quadratic equation

$x^{2} + \frac{x}{\sqrt{2}} + 1 = 0$ .

Accepted Answer

Given quadratic equation is $x^{2} + \frac{x}{\sqrt{2}} + 1 = 0$

Comparing the given quadratic equation to the general form $a x^{2} + b x + c = 0$ , we get
$a = 1, b = \frac{1}{\sqrt{2}} & c = 1$

Substitute these values in below formula
$α = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ or $β = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$ [Assume that, $α, β$ are the roots of the given quadratic equation]
Therefore, $α = \frac{- \frac{1}{\sqrt{2}} + \sqrt{(\frac{1}{\sqrt{2}}) - 4 \times 1 \times 1}}{2 \times 1}$ or $β = \frac{- \frac{1}{\sqrt{2}} - \sqrt{(\frac{1}{\sqrt{2}}) - 4 \times 1 \times 1}}{2 \times 1}$

$\Rightarrow α = \frac{- \frac{1}{\sqrt{2}} + \sqrt{\frac{1}{2} - 4}}{2}$ or $β = \frac{- \frac{1}{\sqrt{2}} - \sqrt{\frac{1}{2} - 4}}{2}$

$\Rightarrow α = \frac{- \frac{1}{\sqrt{2}} + \sqrt{- \frac{7}{2}}}{2}$ or $β = \frac{- \frac{1}{\sqrt{2}} - \sqrt{- \frac{7}{2}}}{2}$

$\Rightarrow α = \frac{- \frac{1}{\sqrt{2}} + i \frac{\sqrt{7}}{\sqrt{2}}}{2}$ or $β = \frac{- \frac{1}{\sqrt{2}} - i \frac{\sqrt{7}}{\sqrt{2}}}{2} [∵ i = \sqrt{- 1}]$

$\Rightarrow α = \frac{- 1 + i \sqrt{7}}{2 \sqrt{2}}$ or $β = \frac{- 1 - i \sqrt{7}}{2 \sqrt{2}}$

Hence, the roots of the given quadratic equation are: $\frac{- 1 \pm i \sqrt{7}}{2 \sqrt{2}}$ .

Solve the following quadratic equation

$x^{2} + \frac{x}{\sqrt{2}} + 1 = 0$ .

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Solve the following quadratic equation x2+x2+1=0.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Solve the following quadratic equation

$x^{2} + \frac{x}{\sqrt{2}} + 1 = 0$ .