If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the mi

If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?

If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?

Step 1: Identify the equation given, which is x^2 + 4x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant (D) is given by the formula D = b^2 - 4ac.
Step 3: In our equation, a = 1, b = 4, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = 4^2 - 4(1)(k).
Step 5: Simplify the expression: D = 16 - 4k.
Step 6: For the roots to be real and equal, the discriminant must be equal to zero: 16 - 4k = 0.
Step 7: Solve the equation 16 - 4k = 0 for k.
Step 8: Rearrange the equation: 4k = 16.
Step 9: Divide both sides by 4: k = 4.
Step 10: Conclude that the minimum value of k for the roots to be real and equal is 4.

Discriminant of a Quadratic Equation – The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. For the roots to be real and equal, D must be equal to zero.
Quadratic Equations – Understanding the standard form of quadratic equations and how to manipulate them to find roots.