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