Question

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 ∅.

Answer 1

it is complex solution

no real number solution

Step-by-step explanation:

13u²+23u=-112

13u²+23u+112=0

a=13, b=23 , c=+112

u= (-b±√(b²-4ac))/2a

u=[(-23±√(23)²-4(13)(112)]/2(13)

u=(-23±√-5295)/26

u=(-23±i√5295)/26

Answer 2

Answer: No real solutions

Note: this is assuming you haven't reached complex numbers yet

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Step-by-step explanation:

The given equation 13u^2+23u = -112 is the same as 13x^2+23x = -112

and we can add 112 to both sides getting 13x^2+23x+112 = 0

We see the equation is in the form ax^2+bx+c = 0

The discriminant is

D = b^2 - 4ac

D = 23^2 - 4(13)(112)

D = -5295

The negative discriminant means there are no real number solutions.

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Extra info:

If D = 0, then there would be exactly one real number solution.

If D > 0, then there would be two distinct real number solutions.