Question

9x2-(a+b)x+(2a2+5ab+2b2)=0 using quadratic formula

Answer 1

I know it's answer. will I tell you

Answer 2

Answer:

Given Quadratic Equation:

9x² - ( a + b )x + ( 2a² + 5ab + 2b² ) = 0

Comparing it with standard form of quadratic equation, lx² + mx + n = 0

we get,

l = 9  ,  m = - ( a + b )   &  n = 2a² + 5ab + 2b²

Solution by quadratic formula is given by,

$x=\frac{-m\pm\sqrt{m^2-4ln}}{2l}$

$x=\frac{-(-(a+b))\pm\sqrt{(-(a+b))^2-4\times9\times(2a^2+5ab+2b^2)}}{2\times9}$

$x=\frac{(a+b)\pm\sqrt{(a+b)^2-36\times(2a^2+5ab+2b^2)}}{18}$

$x=\frac{(a+b)\pm\sqrt{a^2+b^2+2ab-72a^2-180ab-72b^2}}{18}$

$x=\frac{(a+b)\pm\sqrt{-71a^2-178ab-71b^2}}{18}$

$x=\frac{(a+b)\pm\sqrt{71a^2+178ab+71b^2}\,i}{18}$

$x=\frac{(a+b)+\sqrt{71a^2+178ab+71b^2}\,i}{18}$ and $x=\frac{(a+b)-\sqrt{71a^2+178ab+71b^2}\,i}{18}$