Determine the value of |a − b|?
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x^2 + x − 12 = (x − a)(x − b), determine the value of |a − b|.
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My last problem
I dont know how to answer it
x^2 + x − 12 = (x − a)(x − b), determine the value of |a − b|.
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x^2 + x - 12 = (x - a)(x - b)
x^2 + x - 12 = x^2 - ax - bx + ab
x^2 + x - 12 = x^2 - (a + b)x + ab
1 = -(a + b)
-12 = ab
∴ (a + b)^2 - 4ab = 1 - 4(-12) = 1 + 48 = 49
a^2 + 2ab + b^2 - 4ab = 49
a^2 - 2ab + b^2 = 49
(a - b)^2 = 49
√(a - b)^2 = √49
|a - b| = 7.