Question

How do you find the value of the discriminant and determine the number of real-number solutions for this quadratic equation `x^2-11x+30=0`?

Answer 1

The solutions are `S={5,6}`

Explanation:

The equation is `x^2-11x+30`

The discriminant is `Delta=b^2-4ac`
`=(-11)^2-4*1*30=121-120=1`

As, `Delta >0`, we would expect two real roots.

`x=(-b+-sqrtDelta)/(2a)=(11+-1)/2`

So, `x_1=6` and `x_2=5`