Class 10 Math All topics Quadratic Equations

Find the roots of $ax_{2}+bx+c=0(a=0)$ by the method of completing the square.

Solution:

$ax_{2}+bx+c=0$

$⇒ax_{2}+bx+(2a b )_{2}−(2a b )_{2}+c=0$

$⇒(a x+2a b )_{2}−4ab_{2} +c=0$

$⇒(a +2a b )_{2}−(4ab_{2}−ac )_{2}=0$

$⇒(a x+2a b +4ab_{2}−4ac )(a x+2a b −2ab_{2}−4ac )=0$

$a x+2a b +4ab_{2}−4ac =0$, $a x+2a b −2ab_{2}−4ac =0$

$x=2a ⋅a −b+b_{2}−4ac ,x=2a ⋅a −b−b_{2}−4ac $

$∴x=2a−b±b_{2}−4ac $.

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials

introduction to trigonometry

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