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Solve the quadratic:
x2+x-12 = 0
a = 1, b = 1, c = -12
x = | -b ± √b2 - 4ac |
2a |
-b = -(1)
-b = -1
Δ = b2 - 4ac:
Δ = 12 - 4 x 1 x -12
Δ = 1 - -48
Δ = 49 <--- Discriminant
Since Δ > 0, we expect two real roots.
√Δ = √(49)
√Δ = 7
Numerator 1 = -b + √Δ
Numerator 1 = -1 + 7
Numerator 1 = 6
Numerator 2 = -b - √Δ
Numerator 2 = -1 - 7
Numerator 2 = -8
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Solution 1 = | Numerator 1 |
Denominator |
Solution 1 = | 6 |
2 |
Solution 1 = 3
Solution 2 = | Numerator 2 |
Denominator |
Solution 2 = | -8 |
2 |
Solution 2 = -4
(Solution 1, Solution 2) = (3, -4)
(3)2 + 1(3) - 12 ? 0
(9) + 312 ? 0
9 + 312 ? 0
0 = 0
(-4)2 + 1(-4) - 12 ? 0
(16) - 412 ? 0
16 - 412 ? 0
0 = 0