Question

represent (x-2) (3x+5)=2x(x-4) is. a form of quadratic equation​

Answer 1

$x^{2}+7x+10=0$

Step-by-step explanation:

Now, $(x-2)(3x+5)=2x(x-4)$

$\Rightarrow 3x^{2}+5x-6x-10=2x^{2}-8x$

$\Rightarrow 3x^{2}-x+10=2x^{2}-8x$

$\Rightarrow 3x^{2}-2x^{2}-x+8x+10=0$

$\Rightarrow x^{2}+7x+10=0$

This is the required quadratic equation, since the highest power of the variable involved in the equation is 2.

Let us further solve the equation and find its roots.

Here, $x^{2}+7x+10=0$

$\Rightarrow x^{2}+5x+2x+10=0$

$\Rightarrow x(x+5)+2(x+5)=0$

$\Rightarrow (x+5)(x+2)=0$

Thus either $x+5=0$ or $x+2=0$

This gives, $x=-5,-2$

Hence the roots of the given quadratic equation are $x=-5,-2$.