Question

Solve the following equation and find the value of x.
$3{x^2} - x - 4 = 0$

Answer 1

Hint:- Split the middle term of the equation or re-write in such a way that we can solve this equation using factorisation method, that is make it of the form $\left( {x -a} \right)\left( {x - b} \right) = 0$

Complete step-by-step answer:

We have
$3{x^2} - x - 4 = 0$
Now to make it in factor form we will write it as
$3{x^2} - 4x + 3x - 4 = 0$
Now re-writing so that we can take common from the same coefficient terms
$3{x^2} + 3x - 4x - 4 = 0$
Now we can easily take common from it
$3x\left( {x + 1} \right) - 4\left( {x + 1} \right) = 0$
Now we will take (x+1) common from above equation ,then we get
$\left( {x + 1} \right)\left( {3x - 4} \right) = 0$
So x = -1 and $x = \dfrac{4}{3}$
Hence these two are the values of x for which equation is satisfied.

Note: -Whenever we get this type of question the key concept of solving is we have to find x for which equation is satisfied. And this is a quadratic so we can find x directly through formulae $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$ but if it is cubic equation we have to make factor by rearranging and using our brain wisely.