Algebra

 

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions  

 

Combine like terms and arrange equation    

in standard format ax² + bx + c = 0                3x² + (–k) x + 33 = 0    

 

The discriminant is defined as b² – 4ac          (–k)² – (4)(3)(33)    

                                                                          k² – 396    

 

An equation has no real solutions when the discriminant is negative.    

This is because in the quadratic formula, you calculate the square root of the discriminant.    

 

Therefore k² must be smaller than 396 to result in a negative discriminant.    

 

sqrt(396) is 19.9,  The next smaller integer is 19.  So, k = 19 answers the prolblem.         

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