ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equation2 Marks
Question
Form the quadratic equation whose roots are:
$\sqrt{3}$ and $3 \sqrt{3}$
✓
Answer
Let a, β be the roots of the required quadratic equation:
Then, $a =\sqrt{3}$ and $\beta=3 \sqrt{3}$
$a+\beta=\sqrt{3}+3 \sqrt{3} \text { and } a \beta=\sqrt{3} \times 3 \sqrt{3} $
$\therefore a+\beta=4 \sqrt{3} \text { and } a \beta=9$
Required quadratic equation
$x^2-(a+\beta) x+a \beta=0$
$ \Rightarrow x^2-4 \sqrt{3} x+9=0$
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