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Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations1 Mark
MCQ
Choose the correct answer from the given four options in the following questions:
Which constant must be added and subtracted to solve the quadratic equation $9\text{x}^2+\frac{3}{4}\text{x}-\sqrt{2}=0$ by the method of completing the square ?
  • A
    $\frac{1}{8}$
  • ✓
    $\frac{1}{64}$
  • C
    $\frac{1}{4}$
  • D
    $\frac{9}{64}$
✓

Answer

Correct option: B.
$\frac{1}{64}$
Given equation is $9\text{x}^2+\frac{3}{4}\text{x}-\sqrt{2}=0.$
$(3\text{x})^2+\frac{1}{4}(3\text{x})-\sqrt{2}=0$
On putting $3x = y,$ we have $\text{y}^2+\frac{1}{4}\text{y}-\sqrt{2}=0$
$\text{y}^2+\frac{1}{4}\text{y}+\Big(\frac{1}{8}\Big)^2-\Big(\frac{1}{8}\Big)^2-\sqrt{2}=0$
$\Big(\text{y}+\frac{1}{8}\Big)^2=\frac{1}{64}+\sqrt{2}$
$\Big(\text{y}+\frac{1}{8}\Big)^2=\frac{1+64\sqrt{2}}{64}$
Thus, $\frac{1}{64}$ must be added and subtracted to solve the given equation.

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