Use the discriminant to determine the number and type of solutions the equation has? x^2 + 8x + 12 = 0 A.no real solution B.one real solution C. two rational solutions D. two irrational solutions

1 Answer
Srinivas
Mar 13, 2016

C. two Rational solutions

Explanation:

The solution to the quadratic equation
a*x^2 + b*x + c = 0a⋅x2+b⋅x+c=0 is
x = (-b+- sqrt (b^2 - 4*a*c )) / (2* ax=−b±√b2−4⋅a⋅c2⋅a
In the problem under consideration,
a = 1, b = 8 and c = 12
Substituting,
x = (-8+- sqrt (8^2 - 4*1*12 )) / (2* 1x=−8±√82−4⋅1⋅122⋅1
or x = (-8+- sqrt (64 - 48 )) / (2x=−8±√64−482
x = (-8+- sqrt (16)) / (2x=−8±√162
x = (-8+- 4) / (2x=−8±42
x = (-8 + 4) / 2 and x = (-8 - 4) / 2x=−8+42andx=−8−42
x = (- 4) / 2 and x = (-12) / 2x=−42andx=−122
x = - 2 and x = -6x=−2andx=−6

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