To find the possible values of r in the quadratic equation r² + 7r + 8 = 0, we can use the quadratic formula, which is given by:
r = (-b ± √(b² – 4ac)) / 2a
In this equation, a, b, and c are the coefficients from the standard form of the quadratic equation ax² + bx + c = 0. For our equation, we identify:
- a = 1
- b = 7
- c = 8
Next, we need to calculate the discriminant (b² – 4ac):
b² – 4ac = 7² – 4(1)(8)
= 49 – 32
= 17
Since the discriminant is positive (17 > 0), we can conclude that there will be two distinct real roots. Now, we can apply the quadratic formula:
r = (-7 ± √17) / (2 * 1)
= (-7 ± √17) / 2
This gives us the two possible values for r:
- r₁ = (-7 + √17) / 2
- r₂ = (-7 – √17) / 2
So, the possible values of r in the equation r² + 7r + 8 = 0 are:
- r₁ ≈ -2.44 (approximately)
- r₂ ≈ -4.56 (approximately)
In conclusion, the two distinct real roots for the quadratic equation are approximately -2.44 and -4.56.