Question

How to use the discriminant to find out how many real number roots an equation has for `2m^2 - m - 6 = 0`?

Answer 1

See answer

Explanation:

The discriminant, (`Delta`), is derived from quadratic equation:
`x=(b^2+-(sqrt(b^2-4ac)))/(2a)`

Where `Delta` is the expression beneath the root sign, hence:
The discriminant (`Delta`) =`b^2-4ac`

If `Delta`>0 there are 2 real solutions (roots)
If `Delta=0` there is 1 repeated solution (root)
If 0>`Delta` then the equations has no real solutions (roots)

In this case `b=-1`, `c=-6` and `a=2`
`b^2-4ac=(-1)^2-4(2)(-6)=49`

So your equation has two real solutions as `Delta`>0. Using the quadratic formula these turn out to be:

`x=(1+-(sqrt49))/(4)`

`x_1=2`

`x_2=(-6/4)=-1.5`