Given that the discriminant of the equation 4x^2-10x+k=0 is 0,find k
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.
The discriminant (Δ) of a quadratic equation in the form ax^2 + bx + c = 0 can be calculated using the formula:
Δ = b^2 - 4ac
Given the equation 4x^2 - 10x + k = 0, we need to find the value of k when the discriminant is 0. Hence, we know that:
Δ = 0
Substituting the values for a, b, and c into the discriminant formula, we have:
0 = (-10)^2 - 4(4)(k)
Simplifying further:
0 = 100 - 16k
To isolate the variable k, we can subtract 100 from both sides:
-16k = -100
Dividing both sides of the equation by -16:
k = -100 / -16
Simplifying:
k = 25/4
Therefore, the value of k when the discriminant is 0 is 25/4.