iven that (x + 2) and (x - 1) are factors of the quadratic expression below, what are the values of a and b ? 𝑥2+(𝑎+2)𝑥+𝑎+𝑏
Question
Given that
and are factors of the quadratic expression below, what are the values of and ?
Solution
Given that (x + 2) and (x - 1) are factors of the quadratic expression, we can write the expression as:
x^2 + (a + 2)x + a + b = (x + 2)(x - 1)
Expanding the right side, we get:
x^2 + x - 2 = x^2 + (a + 2)x + a + b
Comparing the coefficients on both sides, we get two equations:
1 = a + 2 and -2 = a + b
Solving these equations, we find that a = -1 and b = -3.
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