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1.Find the constant c such that x^2-5x+c is the square of a binomial.

2.The roots of the quadratic x^2+8x+4 are the same as the roots of the quadratic Ax^2+Bx+1. What is A+B?

3.Find the largest integer m such that the equation 5x^2-mx+8=0 has no real solutions.

Please help thank you

 Mar 14, 2020
 #1
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1  Complete the square   

      x^2 - 5x + c        take 1/2 of the x coefficient and square it ...this will be 'c' = 6.25

        (x -2.5)^2                           

 

2    the final term 4 is divided by 4 to get '1'

       divide the whole thing by 4

           1/4 x^2 + 2x + 1      Then add A   and B

 

 

3 if not real solutions , the discriminant must be < 0       b^2 - 4ac <0

                                                                                         m^2 - 4 (5)(8) <0

                                                                                          m^2 - 160 <0                 - 4 sqrt10    <   m <  + 4 sqrt10        m = 12 is greatest integer

 Mar 14, 2020

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