+157 1. Find the constant \(p\) such that \(x^2 - 5x - 2x + p\) is the square of a binomial.
2. Find the constant \(k\) such that the quadratic \(2x^2 + 3x + 8x + k\) has a double root.
3. The roots of \(Ax^2+Bx+1\) are the same as the roots of \(x^2- 3x + 5\). What is \(A+B\)?
4. Find the largest integer \(k\) such that the equation \(5x^2 - kx + 8 - 3x^2 + 15 = 0\) has no real solutions.
Any help is appreciated... thanks a lot.
+129845 2. 2x^2 + 11x + k
We will have a double root when the discriminant = 0
So
11^2 - 4 * 2 * k = 0
121 - 8k = 0
121 = 8k
k = 121/8
+157 That was so fast... they're both correct, thanks so much!!!
Now the harder ones 
+129845 3. x^2 - 3x + 5 = 0
Note that if we just divide through by 5 we get
(1/5)x^2 - (3/5)x + 1 = 0
A =1/5 B =(-3/5)
A + B = 1/5 -3/5 = -2/5
{You can check to see that the roots are the same }
+129845 4. Simplified we get
2x^2 -kx + 23 = 0
We have no real solutions when the discriminant is < 0
So
k^2 - 4(2)(23) < 0
k^2 - 184 < 0
k^2 < 184
k < sqrt (184) ≈ 13.564
So the largest integer = 13
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