Question

Solve the following quadratic equation by factorization.
$3x^2-14x-5=0$

Answer 1

Given quadratic equation is $3x^2-14x-5=0$

For splitting the middle term, we have to select the two terms such that, their sum is $-14x$ [Since, the middle term is $-14x$ and their product is $3x^2\times (-5)=-15x^2$.

So the terms are $-15x$ and $+x$. [Since, $-15x+x=-14x,-15x\times x=-15x^2$]

Now, lets solve $3x^2-14x-5=0$

$\Rightarrow 3x^2-15x+x-5=0$

$\Rightarrow 3x(x-5)+1(x-5)=0$

$\Rightarrow (x-5)(3x+1)=0$

$\Rightarrow x-5=0$ or $3x+1=0$

$\Rightarrow x=5$ or $x=-\frac{1}{3}$

Therefore, the roots of the quadratic equation is $3x^2-14x-5=0$ are $5,-\frac{1}{3}$.