Question

For problems 1 – 4, use the discriminant to determine the nature of the roots.

Answer 1

The Discriminant = b²-4ac
1.
a=2
b= 5
c=-3
The Discriminant is 49
When a, b and c are real numbers, a ≠ 0 and discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real, rational unequal.

2.
a=-1
b=1
c=1
The Discriminant is 5
When a, b and c are real numbers, a ≠ 0 and discriminant is positive but not a perfect square then the roots of the quadratic equation ax2 + bx + c = 0 are real, irrational and unequal.

3.
a=1
b=6
c=11
The Discriminant is-8
then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and imaginary.

4.
a=9
b=-54
c=81
The Discriminant is 0
the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and equal.