We have: nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; #160; #160; #160; #160;x2 #160; #160;4x #160;+ #160;7 #160;= ...

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

Inequalities Involving Modulus Function

x 2-4 x+7=0

Question

$x^{2} - 4 x + 7 = 0$

Open in App

Solution

We have:
$x^{2} - 4 x + 7 = 0 \Rightarrow x^{2} - 4 x + 4 + 3 = 0 \Rightarrow x^{2} - 2 \times x \times 2 + 2^{2} - (\sqrt{3} i)^{2} = 0 \Rightarrow (x - 2)^{2} - (\sqrt{3} i)^{2} = 0 \Rightarrow (x - 2 + \sqrt{3} i) (x - 2 - \sqrt{3} i) = 0$

$\Rightarrow (x - 2 + \sqrt{3} i) = 0$ or, $(x - 2 - \sqrt{3} i) = 0$
$\Rightarrow x = 2 - \sqrt{3} i$ or, $x = 2 + \sqrt{3} i$

Hence, the roots of the equation are $2 \pm i \sqrt{3}$ .

Suggest Corrections

Similar questions

Solve the following quadratics $x^{2} - 4 x + 7 = 0$

α, β

x^{2} - 3 x + 5 = 0

(α^{2} - 3 α + 7) and (β^{2} - 3 β + 7)

x^{2} + 4 x + 2 y - 7 = 0

Join BYJU'S Learning Program