For the quadratic equation 2x^2 - 4x + k = 0 to have equal roots, what must be t

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Question: For the quadratic equation 2x^2 - 4x + k = 0 to have equal roots, what must be the value of k? (2019)

Options:

Correct Answer: 4

Exam Year: 2019

Solution:

For equal roots, the discriminant must be zero: (-4)^2 - 4*2*k = 0. Solving gives k = 4.

For the quadratic equation 2x^2 - 4x + k = 0 to have equal roots, what must be the value of k? (2019)

For the quadratic equation 2x^2 - 4x + k = 0 to have equal roots, what must be the value of k? (2019)

Step 1: Identify the quadratic equation, which is 2x^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 = 2, b = -4, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = (-4)^2 - 4*2*k.
Step 5: Calculate (-4)^2, which is 16, so we have D = 16 - 4*2*k.
Step 6: Simplify 4*2 to get 8, so now we have D = 16 - 8k.
Step 7: For the roots to be equal, the discriminant must be zero, so set D = 0: 16 - 8k = 0.
Step 8: Solve for k by moving 8k to the other side: 16 = 8k.
Step 9: Divide both sides by 8 to find k: k = 16 / 8.
Step 10: Simplify 16 / 8 to get k = 2.

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 equal to zero.
Quadratic Equations – Understanding the standard form of quadratic equations and the conditions for their roots (real, equal, or complex).