-Find all values of k for which the equation 3x^2−4x+k=0 has no solutions.
-What is the value of m, if the equation my^2+2y−4=0 has exactly one root?
i don't get it I don't get it somebody help ahhhhh i can't take it anymore
+128664 3x^2 - 4x + k = 0 will always have solutions.....but....if you mean real solutions, we can use the discriminant to find the values of k that produce these
(-4)^2 - 4(3)k ≥ 0
16 - 12k ≥ 0 divide through by 4
4 - 3k ≥ 0 add 3k to both sides
4 ≥ 3k divide both sides by 3
4/3 ≥ k .......this means that k must be ≤ 4/3 for the function to have real solutions
my^2 + 2y - 4 = 0 ....we need to find the value of m that makes the discriminant = 0
(2)^2 - 4(m)(-4) = 0
4 + 16m = 0 divide through by 4
1 + 4m = 0 subtract 4m from both sides
1 = -4m divide both sides by -4
-1 / 4 = m
Thus.....the given function will have exactly one root [ of a multiplicity of 2] when m = -1/4
