Question
Solve using formula.
$5 m^2-4 m-2=0$
$5 m^2-4 m-2=0$
✓
Answer
$5 m^2-4 m-2=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =5, b=-4 \text { and } c=-2$
$ \therefore b ^2-4 ac =(-4)^2-4(5)(-2) $
$=16+40 $
$=56 $
$ m=\frac{- b \pm \sqrt{ b ^2-4 a c}}{2 a } $
$ \Rightarrow m =\frac{-(-4) \pm \sqrt{56}}{2 \times 5}$
$ \Rightarrow m =\frac{4 \pm 2 \sqrt{14}}{10} $
$\Rightarrow m =\frac{4+2 \sqrt{14}}{10} \text { or } m =\frac{4-2 \sqrt{14}}{10} $
$\Rightarrow m =\frac{2+\sqrt{14}}{5} \text { or } m =\frac{2-\sqrt{14}}{5}$
$ \Rightarrow a =5, b=-4 \text { and } c=-2$
$ \therefore b ^2-4 ac =(-4)^2-4(5)(-2) $
$=16+40 $
$=56 $
$ m=\frac{- b \pm \sqrt{ b ^2-4 a c}}{2 a } $
$ \Rightarrow m =\frac{-(-4) \pm \sqrt{56}}{2 \times 5}$
$ \Rightarrow m =\frac{4 \pm 2 \sqrt{14}}{10} $
$\Rightarrow m =\frac{4+2 \sqrt{14}}{10} \text { or } m =\frac{4-2 \sqrt{14}}{10} $
$\Rightarrow m =\frac{2+\sqrt{14}}{5} \text { or } m =\frac{2-\sqrt{14}}{5}$
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