Maharashtra BoardEnglish MediumSTD 10MathsP-1 Quadratic Equations4 Marks
Question
Solve the following quadratic equation.
$x^2-4 x-3=0$
✓
Answer
$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 ac =-4^2-4(1)(-3) $
$=16+12 $
$=28 $
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a } $
$\Rightarrow x =\frac{4 \pm \sqrt{28}}{2 \times 1} $
$\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} $
$\Rightarrow x=2+\sqrt{7} \text { or } x=2-\sqrt{7}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.