Im lost i don't know how to do this can someone show me step by step how to solve this
For what value does c does the equation have one real root? Hint using the values of a and b found in the equation, solve D = 0 for c.
Consider the quadratic expression X^2 + 4x + c = 0.
There is no a, b or D shown in the equation.
x^2 + 4x + 4 = (x+2)^2
To find the value of c that makes the equation have one real root, we need to use the discriminant (D) of the quadratic equation. The discriminant is calculated using the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 4, and c is the value we want to find.
Step 1: Set up the equation for calculating the discriminant
D = b^2 - 4ac
Step 2: Substitute the values of a, b, and c into the equation
D = (4)^2 - 4(1)(c)
D = 16 - 4c
Step 3: Set the discriminant equal to zero, since we want to find the value of c that results in one real root
0 = 16 - 4c
Step 4: Solve for c
4c = 16
c = 16/4
c = 4
Therefore, when c = 4, the equation X^2 + 4x + c = 0 will have one real root.