Question

Form the equation whose roots are $0,\pm a,\frac{c}{b}$.

Answer 1

The roots of the required equation are $0,\pm a,\frac{c}{b}$

So the equation should be divisible by $x,(x-a),(x+a),(x-\frac{c}{b})$

So the required equation is $x(x-a)(x+a)(x-\frac{c}{b})=0$

$\Rightarrow (x^2-\frac{c}{b}x)(x^2-a^2)=0$

$\Rightarrow x^4-\frac{c}{b}{x}^3-a^2{x}^2+\frac{c{a}^2}{b}x=0$

$\Rightarrow b{x}^4-c{x}^3-a^{2}b{x}^2+a^{2}cx=0$