Question

Find the roots of 4x2 + 3x + 5 = 0 by the method of completing the
square.​

Answer 1

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Answer 2

$\large\bf\underline{Given:-}$

• equation :- 4x² + 3x + 5

$\large\bf\underline {To \: find:-}$

• Roots of the given equation by completing the square method.

$\huge\bf\underline{Solution:-}$

• 4x² + 3x + 5 = 0

$\rm \dashrightarrow \: 4 {x}^{2} + 3x + 5 = 0 \\ \\ \rm\text { \dag \: Divide both side by 4} \\ \\ \dashrightarrow \rm \: \frac{4 {x}^{2} }{4} + \frac{3x}{4} + \frac{5}{4} = \frac{0}{4} \\ \\ \dashrightarrow \rm \: {x}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\ \rm Add \: (\frac{ 3}{8}) {}^{2} \: on \: both \: side \\ \\ \rm \dashrightarrow \: {x}^{2} + \frac{3x}{4} + \frac{9}{64} = - \frac{5}{4} + \frac{9}{64} \\ \\ \rm \dashrightarrow \:(x + \frac{3}{8} ) {}^{2} = \frac{ - 80 + 9}{64} \\ \\ \rm \dashrightarrow \:(x + \frac{3}{8} ) {}^{2} = \frac{ - 71}{64} \\ \\ \rm \dashrightarrow \:x + \frac{ 3}{8} = \sqrt{ \frac{ - 71}{64} } \\ \\ \rm \dashrightarrow \:x + \frac{3}{8} = \frac{ \pm\sqrt{71} }{8} \\ \\ \rm \dashrightarrow \:x = \frac{ \pm\sqrt{71} }{8} - \frac{3}{8} \\ \\ \rm \dashrightarrow \:x = \frac{ \sqrt{71 } - 3 }{8} \: or \: x = \frac{ - ( \sqrt{71} + 3) }{8}$

So, the roots of the given equation are:-

• x = √71-3/8
• x = -(√71+3)/8