Question
Given that the discriminant of the equation 4x^2-10x+k=0 is 0,find k
Answers
GPT 3.5
The discriminant of a quadratic equation Ax^2 + Bx + C = 0 is given by Δ = B^2 - 4AC.
In this case, the equation is 4x^2 - 10x + k = 0.
So, A = 4, B = -10, and C = k.
The discriminant is Δ = (-10)^2 - 4(4)(k) = 100 - 16k.
Since we are given that the discriminant is 0, we can set Δ = 0:
100 - 16k = 0.
Solving for k:
16k = 100,
k = 100/16,
k = 25/4.
Therefore, k = 25/4.
In this case, the equation is 4x^2 - 10x + k = 0.
So, A = 4, B = -10, and C = k.
The discriminant is Δ = (-10)^2 - 4(4)(k) = 100 - 16k.
Since we are given that the discriminant is 0, we can set Δ = 0:
100 - 16k = 0.
Solving for k:
16k = 100,
k = 100/16,
k = 25/4.
Therefore, k = 25/4.