Discriminant — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
b2 - 4ac. Its sign counts the real solutions.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
Practise this idea
7 questions in the course bank use Discriminant, in Solving Quadratic Equations, Complex Numbers.
Problem 1
Solve x2 + 4x - 5 = 0 using the quadratic formula.
Worked answer
1 and -5
b2 - 4ac = 16 + 20 = 36
x = -4 ± 62
x = 1 or x = -5
Problem 2
Solve 2x2 - 5x - 3 = 0.
Worked answer
3 and -1/2
25 + 24 = 49
x = 5 ± 74
x = 3 or x = -12
Problem 3
Find the discriminant of x2 - 6x + 9 = 0 and say how many real solutions there are.
Worked answer
0, one solution
36 - 36 = 0
Zero means one repeated solution
x = 3
Problem 4
How many real solutions does x2 + 2x + 5 = 0 have?
Worked answer
none
4 - 20 = -16
Negative, so no real solutions
The parabola misses the x-axis
Problem 5
Solve x2 - 4x + 1 = 0, leaving the answer exact.
Worked answer
2 + sqrt(3) and 2 - sqrt(3)
16 - 4 = 12
x = 4 ± √122 = 4 ± 2√32
x = 2 ± √3
Problem 6
For what value of k does x2 + kx + 9 = 0 have exactly one solution, with k > 0?
Worked answer
6
k2 - 36 = 0
k2 = 36
k = 6 since k > 0
Problem 7
How many real roots does x2+2x+5=0 have?
- None — both roots are complex
- One
- Two
- Three
Worked answer
None — both roots are complex
4-20=-16
Negative discriminant means no real roots