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

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

then the solution is given by:

`x = (-b \pm √(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 = (-(-1) \pm √((-1)^2-4(3)(-11)))/(2(3))`

⇒
`x = (1 \pm √(1+132))/(6)`

⇒
`x = (1 \pm √(133))/(6)`

Therefore, the solution for the given equations are:

`x = (1 + √(133))/(6)`,
`(1 -√(133))/(6)`