Find the largest integer k such that the equation 5x^2 - kx + 88 = 0 has no real solutions.
+2407 Hi Guest!
Background
To solve this question, we should use the quadartic equation.
If you don't know what that is, here's a wiki page: https://en.wikipedia.org/wiki/Quadratic_equation
Whether or not a quadratic has a real answer is based on it's discriminant, b^2 - 4ac.
If the discriminant is negative, then the solutions won't work since you can't square root a negative number.
Equation
5x^2 - kx + 88 = 0
Discriminant
b^2 - 4ac
(-k)^2 - 4(5)(88)
Solving
So, we're looking for the greatest k value where (-k)^2 - 4(5)(88) is negative and an integer.
(-k)^2 - 4(5)(88)
k^2 - 1760 < 0
k^2 < 1760
k < sqrt(1760)
The largest integer that fufils this is 41.
Answer
Thus, our answer is 41.
I hope this helped. :))))
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