The equation you’re looking at, x² + 1x – 90 = 0, is a quadratic equation. Quadratic equations can often be solved using the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In this case, the coefficients are:
- a = 1 (the coefficient of x²)
- b = 1 (the coefficient of x)
- c = -90 (the constant term)
Now, let’s calculate the discriminant:
b² – 4ac = 1² – 4(1)(-90)
= 1 + 360
= 361
Since the discriminant is positive, we will have two distinct real solutions. Now we can substitute back into the quadratic formula:
x = (-1 ± √361) / (2 * 1)
= (-1 ± 19) / 2
This gives us two potential solutions:
x₁ = (-1 + 19) / 2 = 18 / 2 = 9
x₂ = (-1 – 19) / 2 = -20 / 2 = -10
Thus, the solutions to the equation are a = 9 and b = -10. Therefore, we can conclude:
- a = 9
- b = -10
This means that the values of a and b that satisfy the equation are indeed 9 and -10.