Solve the following quadratic equation. x2 – 4x – 3 = 0 - Vidyadip

Question

Solve the following quadratic equation.
x² – 4x – 3 = 0

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Answer

$\begin{array}{l}x^2-4 x-3=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=1, b=-4 \text { and } c=-3 \\ \therefore b^2-4 a c=-4^2-4(1)(-3) \\ =16+12 \\ =28 \\ x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\ \Rightarrow x=\frac{4 \pm \sqrt{28}}{2 \times 1}\end{array}$
$\begin{array}{l}\Rightarrow x=\frac{4 \pm 2 \sqrt{7}}{2} \\ \Rightarrow x=\frac{4+2 \sqrt{7}}{2} \text { or } x=\frac{4-2 \sqrt{7}}{2} \\ \Rightarrow x=\frac{2(2+\sqrt{7})}{2} \text { or } x=\frac{2(2-\sqrt{7})}{2} \\ \Rightarrow x=2+\sqrt{7} \text { or } x=2-\sqrt{7}\end{array}$

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