Question

Evaluate the discriminant for the equation. Determine the number of real solutions 6x^2 + x + 3=0

Answer 1

The given equation is

`6x^2+x+3=0`

it is of the from

`ax^2+bx+c=0`

where a=6 , b=1 and c=3

Consider the quadratic formula

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Recall that the discriminant of the quadratic equation is the part of the underneath square root of the formula

`discriminant=b^2-4ac`

Substitute a=6,b=1 and c=3, we get

`discriminant=1-4*6*3=-71<0`
`\text{If }discriminant=b^2-4ac<0\text{ then the }quadratic\text{ }equation\text{ has no real solutions.}`

Discriminant=-71

Hence there is no solution.