What is the value of k for which the equation x^2 - 4x + k = 0 has roots that ar
Practice Questions
Q1
What is the value of k for which the equation x^2 - 4x + k = 0 has roots that are equal?
4
8
16
0
Questions & Step-by-Step Solutions
What is the value of k for which the equation x^2 - 4x + k = 0 has roots that are equal?
Step 1: Identify the equation given, which is x^2 - 4x + k = 0.
Step 2: Understand that for a quadratic equation to have equal roots, the discriminant must be zero.
Step 3: Recall the formula for the discriminant, which is given by D = b^2 - 4ac, where a, b, and c are the coefficients from the equation ax^2 + bx + c.
Step 4: In our equation, a = 1, b = -4, and c = k.
Step 5: Substitute the values of a and b into the discriminant formula: D = (-4)^2 - 4*1*k.
Step 6: Calculate (-4)^2, which is 16, so we have D = 16 - 4k.
Step 7: Set the discriminant equal to zero for equal roots: 16 - 4k = 0.
Step 8: Solve for k by adding 4k to both sides: 16 = 4k.
Step 9: Divide both sides by 4 to isolate k: k = 16 / 4.
