Question

Form the equation whose roots are $2,-3$ and $\frac{7}{5}$.

Answer 1

Given that the roots of required equation is $2,-3,\frac{7}{5}$

Since $2,-3,\frac{7}{5}$ are roots of the equation, the required equation should be divisible by $x-2$, $x+3$ and $x-\frac{7}{5}$

So the required equation is $(x-2)(x+3)(x-\frac{7}{5})=0$

$\Rightarrow (x^2+x-6)(x-\frac{7}{5})=0$

$\Rightarrow x^3-\frac{2}{5}{x}^2-\frac{37}{5}x+\frac{42}{5}=0$

$\Rightarrow 5x^3-2x^2-37x+42=0$