Question

what are the solutions of the quadratic equation below? 3x2 - x = 11

Answer 1

I hope this helps you



3x^2-x-11=0


disctirminant = (-1)^2-4.3. (-11)



disctirminant =1+132=133



x1= -(-1)+ square root of 133/2.3


x1= 1+ square root of 133/6


x2= -(-1) - square root of 133/2.3


x2= 1- square root of 133/6

Answer 2

Answer:

A quadratic equation  $ax^2+bx+c=0$       ....[1]

then the solution is given by:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Given the equation:

$3x^2-x =11$

Subtract 11 from both sides we have;

$3x^2-x-11 =0$

On comparing with [1] we have;

a = 3 , b  =-1 and c =-11

Substitute these we have;

$x = \frac{-(-1) \pm \sqrt{(-1)^2-4(3)(-11)}}{2(3)}$

⇒$x = \frac{1 \pm \sqrt{1+132}}{6}$

⇒$x = \frac{1 \pm \sqrt{133}}{6}$

Therefore, the solution for the given equations are:

$x = \frac{1 + \sqrt{133}}{6}$, $\frac{1 -\sqrt{133}}{6}$