Question

Determine the number of real and imaginary roots of the following polynomial $a{x}^2+b{x}^2+cx+d=0$

Answer 1

$a{x}^2+b{x}^2+cx+d=0$

$(a+b)x^2+cx+d=0$

to find the roots:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Values of a,b and c from given equation are:

$a=(a+b),b=c$ and $c=d$

Substituting the values of a,b and c in the formula, we get,

$\frac{-c\pm \sqrt{c^2-4(a+b)d}}{2(a+b)}$

if $\sqrt{b^2-4ac}>0$ we have 2 real roots

$\frac{-c+\sqrt{b^2-4ac}}{2(a+b)}$ and $\frac{-c-\sqrt{b^2-4ac}}{2(a+b)}$

if $\sqrt{b^2-4ac}<0$ we have 2 imaginary roots

$\frac{-c+i\sqrt{b^2-4ac}}{2(a+b)}$ and $\frac{-c-i\sqrt{b^2-4ac}}{2(a+b)}$