Question

4x2-5x+2=0 solve using completing the square method​

Answer 1

Answer:

4×2-5x+2=0

=8+2=-5x

=10=5x

=x=2

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{\frac{5+\sqrt-{7}}{8} \ and \ \frac{5-\sqrt{-7}}{8} \ are \ roots \ of \ the \ equation.}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{4x^{2}-5x+2=0}}$

$\sf\pink{To \ find:}$

$\sf{The \ roots \ of \ the \ equation.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{4x^{2}-5x+2=0}}$

$\sf{Divide \ equation \ through \ by \ 4}$

$\sf{\implies{x^{2}-\frac{5x}{4}+\frac{1}{2}=0}}$

$\sf{\implies{x^{2}-\frac{5x}{4}=-\frac{1}{2}}}$

___________________________________

$\sf{(\frac{1}{2}\times \ Coefficient \ of \ x)^{2}}$

$\sf{\implies{(\frac{1}{2}\times\frac{5}{4})^{2}}}$

$\sf{\implies{(\frac{5}{8})^{2}}}$

$\sf{\implies{\frac{25}{64}}}$

____________________________________

$\sf{Add \ \frac{25}{64} \ on \ both \ sides \ of \ equation.}$

$\sf{\implies{x^{2}-\frac{5x}{4}+\frac{25}{64}=-\frac{1}{2}+\frac{25}{64}}}$

$\sf{\implies{x^{2}-\frac{5x}{4}+\frac{25}{64}=\frac{-32+25}{64}}}$

$\sf{\implies{(x-\frac{5}{8})^{2}=\frac{-7}{64}}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{\implies{x-\frac{5}{8}=\frac{\sqrt{-7}}{8} \ or \ -\frac{\sqrt{-7}}{8}}}$

$\sf{\implies{x=\frac{5}{8}+\frac{\sqrt{-7}}{8} \ or \ \frac{5}{8}-\frac{\sqrt{-7}}{8}}}$

$\sf{\implies{x=\frac{5+\sqrt{-7}}{8} \ or \ \frac{5-\sqrt{-7}}{8}}}$

$\sf\purple{\tt{\therefore{\frac{5+\sqrt{-7}}{8} \ and \ \frac{5-\sqrt{-7}}{8} \ are \ roots \ of \ the \ equation.}}}$