To find the greater root of the quadratic equation x² + 13x + 12 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
Here, the coefficients are:
- a = 1
- b = 13
- c = 12
Now, we need to calculate the discriminant (b² – 4ac):
b² = 13² = 169
4ac = 4 * 1 * 12 = 48
Discriminant = 169 – 48 = 121
Since the discriminant is positive, there are two real roots. Now we can plug the values into the quadratic formula:
x = (-13 ± √121) / 2
x = (-13 ± 11) / 2
This gives us two potential roots:
- x₁ = (-13 + 11) / 2 = -2 / 2 = -1
- x₂ = (-13 – 11) / 2 = -24 / 2 = -12
Therefore, the roots of the equation are -1 and -12. The greater root is -1.