If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of
Practice Questions
Q1
If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
0
4
8
16
Questions & Step-by-Step Solutions
If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
Step 1: Identify the quadratic equation given, which is x^2 - 4x + k = 0.
Step 2: Recall that for a quadratic equation ax^2 + bx + c = 0, the discriminant 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: Calculate (-4)^2, which is 16, so now we have D = 16 - 4k.
Step 6: For the roots to be equal, the discriminant must be zero. Set the equation to zero: 16 - 4k = 0.
Step 7: Solve for k by adding 4k to both sides: 16 = 4k.
Step 8: Divide both sides by 4 to isolate k: k = 16 / 4.
Step 9: Calculate 16 / 4, which equals 4. Therefore, k = 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 equation to have equal roots, the discriminant must be zero.
Quadratic Equations – Understanding the standard form of a quadratic equation and how to manipulate it to find specific values.
