Question

please solve this equation:
3x²-x-24=0 and give the value of x​

Answer 1

Answer:

The values of $x$ are   $3$  or  $\frac{-8}{3}$ .

Step-by-step explanation:

This is a quadratic equation of the form $ax^{2} +bx+c=0$,

where  $a=3,\ b=-1,\ c=-24$.

Since it is a quadratic equation, $x$ has two values.

We are asked to fin the value of $x$, value of $x$ is also known as roots of the equation or zeroes of the equation.

There are three methods to solve a quadratic equation.

1. Factorization method
2. Using the quadratic formula
3. Completing the square method.

Here we use quadratic formula to find the value of $x$ .

That is $x=\frac{-b}{2a}$ ± $\frac{\sqrt{b^{2}-4ac } }{2a}$ .

First find the discriminant

             $b^{2} -4ac=(-1)^{2} -4(3)(-24)$

                           $=1+288\\\\=289$

Therefore

$x=\frac{1}{6}$ ±$\frac{\sqrt{289} }{6}$

  $=\frac{1}{6}$ ± $\frac{17}{6}$

  $= \frac{1+17}{6}$  or  $\frac{1-17}{6}$

  $=\frac{18}{6}$   or   $\frac{-16}{6}$

  $=3$   or   $\frac{-8}{3}$

Thus the values of $x$ are   $3\ or\ \frac{-8}{3}$

Hence the answer

thank you