+0  
 
0
70
1
avatar

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

 Jan 12, 2021
 #1
avatar+843 
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. :))))

=^._.^=

 Jan 12, 2021

32 Online Users

avatar
avatar
avatar
avatar
avatar