Find the roots of 2x^2-7x+3=0 quadratic equations, if they exist, by the method of completing the square ?

byAmlesh Mahato •November 13, 2021

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Solution:

⇒ Given

$⇒From Discriminant Formula,Chapter-4,Exercise-4.3,Math- Class 10,$

∴ a = 2, b = -7, c = 3

⇒From Discriminant Formula

$⇒From Discriminant Formula$

$\large =\left ( -7 \right )^{2}-4\times 2\times 3$

$\large =49-24$

$\large \Rightarrow 25\geq 0$

⇒Equation Have Two real roots

⇒Finding Roots By Completing Square Method

$Find the roots of 2x^2-7x+3=0 quadratic equations, if they exist, by the method of completing the square ?$

$⇒Finding Roots By Completing Square Method$ $⇒Finding Roots By Completing Square Method$

$⇒Finding Roots By Completing Square Method$

$⇒Finding Roots By Completing Square Method$

$\large \Rightarrow \left ( \sqrt{2}x-\frac{7}{ 2\sqrt{2}}\right )^{2}=\frac{49-24}{8}$

$\large \Rightarrow \left ( \sqrt{2}x-\frac{7}{ 2\sqrt{2}}\right )^{2}=\frac{25}{8}$

$\large \Rightarrow \left ( \sqrt{2}x-\frac{7}{ 2\sqrt{2}}\right )^{2}=\left ( \frac{5}{2\sqrt{2}} \right )^{2}$

$\large \Rightarrow \sqrt{2}x-\frac{7}{ 2\sqrt{2}}=\pm \frac{5}{2\sqrt{2}}$

$\large \Rightarrow \sqrt{2}x=\frac{7}{ 2\sqrt{2}}+ \frac{5}{2\sqrt{2}},\frac{7}{ 2\sqrt{2}}- \frac{5}{2\sqrt{2}}$

$\large \Rightarrow \sqrt{2}x=\frac{12}{ 2\sqrt{2}},\frac{2}{ 2\sqrt{2}}$

$\large \Rightarrow \sqrt{2}x=\frac{6}{ \sqrt{2}},\frac{1}{ \sqrt{2}}$

$\large \Rightarrow x=\frac{6}{ \sqrt{2}\times \sqrt{2}},\frac{1}{ \sqrt{2}\times \sqrt{2}}$

$\large \Rightarrow x=\frac{6}{2},\frac{1}{2}$

$\large \Rightarrow x=3,\frac{1}{2}$

Tags: Chapter-4 Exercise-4.3 Math- Class 10