Question

The discriminant of a general quadratic equation ax²+bx+c = 0, where a≠0, is given by D = b²−4ac. 

i.   State three possibilities of the discriminant.

ii.   Use the discriminant to determine how many real solutions the equation 2x² −10x + 20 = 0 have?   

Answer 1

1)If D>0, we will have 2 different real numbers.

If D=0, we will have 2 equal numbers.

If D<0, we will have complex conjugate numbers

2)

$2x^2-10x+20=0\\ x^2-5x+10=0\\ D=25-40<0$

It means that equation won't have a solution in real numbers