Find the largest integer k such that the equation 5x^2 - kx + 88 = 0 has no real solutions.

Guest Jan 12, 2021

#1**0 **

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. :))))

=^._.^=

catmg Jan 12, 2021