Solve the quadratic:
n2-4n-21 = 0
Set up the a, b, and c values:
a = 1, b = -4, c = -21
Quadratic Formula
| n = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(-4)
-b = 4
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = -42 - 4 x 1 x -21
Δ = 16 - -84
Δ = 100 <--- Discriminant
Since Δ > 0, we expect two real roots.
Take the square root of Δ
√Δ = √(100)
√Δ = 10
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = 4 + 10
Numerator 1 = 14
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = 4 - 10
Numerator 2 = -6
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
| Solution 1 = | 14 |
| 2 |
Solution 1 = 7
Solution 2
| Solution 2 = | Numerator 2 |
| Denominator |
| Solution 2 = | -6 |
| 2 |
Solution 2 = -3
Solution Set
(Solution 1, Solution 2) = (7, -3)
Prove our first answer
(7)2 - 4(7) - 21 ? 0
(49) - 2821 ? 0
49 - 2821 ? 0
0 = 0
Prove our second answer
(-3)2 - 4(-3) - 21 ? 0
(9) + 1221 ? 0
9 + 1221 ? 0
0 = 0
Final Answer
(Solution 1, Solution 2) = (7, -3)
