Question

For the quadratic equation h=kx2+4x+5 to have only one x-intercept, what should be the possible value(s) of k?

A) k=0
B) k=0
C) k>0
D) k<0

Answer 1

The value of k for the quadratic equation h=kx2+4x+5 to have only one x-intercept must be 0.2, determined by setting the discriminant to zero.

Step-by-step explanation:

To determine the value(s) of k for the quadratic equation h = kx2+4x+5 to have only one x-intercept, we need to look at the discriminant of the equation, which is found in the quadratic formula. The discriminant is the part b2 - 4ac in the quadratic equation ax2 + bx + c = 0. For a quadratic equation to have exactly one solution, the discriminant must be equal to zero. This means that 42 - 4(k)(5) must equal zero. Solving for k, we get 16 - 20k = 0, leading to k = 4/20, which simplifies to k = 1/5 or k = 0.2. Therefore, for the original equation to have one x-intercept, k must be equal to 0.2.