The function g(x) = 4x^2 - 4x + m has exactly one zero. What is the value of m?
For what values of k does the equation 3x^2 + 4x + k = 0 have no real roots? One real root? Two real roots?
+128474 4x^2 - 4x + m
If this has one zero.....then the discriminant = 0 ....so....
(-4)^2 - 4(4)m = 0
16 - 16m = 0
16 = 16m divide both sides by 16
1 = m
+128474 For what values of k does the equation 3x^2 + 4x + k = 0 have no real roots? One real root? Two real roots?
No real roots if the discriminant is < 0 ....so....
(-4)^2 - 4(3)(k) < 0
16 - 12k < 0
16 < 12k
4/3 < k
k > 4/3
One real root if the disriminant = 0
(-4)^2 - 4(3)k = 0
16 - 12k = 0
16 = 12k
4/3 = k
It's obvious that we must have two real roots if k < 4/3
