Solve 13u2+23u=−112 by using the quadratic formula. Give an exact answer and simplify any fractions. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.
Mathematics · High School · Tue Nov 03 2020
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Given the quadratic equation:
13u^2 + 23u = -112
It can be written as,
12u^2 + 23u + 112 = 0
Determine the factors by using the quadratic formula.
Quadratic formula:
(-b + - √(b^2-4ac))/2a
a = 12
b = 23
c= 112
Solution:
Substitute the values of a, b and c in the quadratic formula.
(-b + - √(b^2-4ac))/2a
(-23 + - √((23)^2-4(12)(112)))/ 2(12)
(-23 + - √(529- 5376))/ 24
(-23 + - √(-4847))/ 24
It is a common rule that when the value inside the square root sign of the equation of quadratic formula is negative or b^2 -4ac < 0, then the number will have no real solution. This is because we cannot take the square root of a negative number, thus it contains no real solution.
Final answer:
∅ or no real solutions