Changing the subject of a formula — MATHEMATICS STD 9 — Question
ICSE BoardEnglish MediumSTD 9MATHEMATICSChanging the subject of a formula4 Marks
Question
Make $c$ the subject of formula $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$
✓
Answer
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$\Rightarrow 2 a x=-b \pm \sqrt{b^2-4 a c} $
$\Rightarrow 2 a x+b= \pm \sqrt{b^2-4 a c}$
Taking square both sides
$\Rightarrow(2 a x+b)^2=b^2-4 a c $
$\Rightarrow 4 a c=b^2-(2 a x+b)^2 $
$\Rightarrow c=\frac{b^2-(2 a x+b)^2}{4 a} .$
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