For the quadratic equation x^2 - 6x + k = 0 to have equal roots, what must be the value of k?
Practice Questions
1 question
Q1
For the quadratic equation x^2 - 6x + k = 0 to have equal roots, what must be the value of k?
6
9
12
0
Setting the discriminant to zero: (-6)^2 - 4*1*k = 0 gives k = 9.
Questions & Step-by-step Solutions
1 item
Q
Q: For the quadratic equation x^2 - 6x + k = 0 to have equal roots, what must be the value of k?
Solution: Setting the discriminant to zero: (-6)^2 - 4*1*k = 0 gives k = 9.
Steps: 8
Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c = 0. Here, a = 1, b = -6, and c = k.
Step 2: Recall that for a quadratic equation to have equal roots, the discriminant must be zero. The discriminant is given by the formula D = b^2 - 4ac.
Step 3: Substitute the values of a and b into the discriminant formula: D = (-6)^2 - 4*1*k.
Step 4: Calculate (-6)^2, which equals 36. So, the equation becomes 36 - 4*k.
Step 5: Set the discriminant equal to zero for equal roots: 36 - 4*k = 0.
Step 6: Solve for k by rearranging the equation: 4*k = 36.
Step 7: Divide both sides by 4 to find k: k = 36 / 4.
Step 8: Calculate 36 / 4, which equals 9. Therefore, k must be 9.
