For the quadratic equation 2x^2 + 4x + k = 0 to have real and equal roots, what
Practice Questions
Q1
For the quadratic equation 2x^2 + 4x + k = 0 to have real and equal roots, what is the condition on k? (2020)
k < 0
k = 0
k = 8
k > 8
Questions & Step-by-Step Solutions
For the quadratic equation 2x^2 + 4x + k = 0 to have real and equal roots, what is the condition on k? (2020)
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 - 8k.
Step 6: For the roots to be real and equal, the discriminant must be equal to zero: 16 - 8k = 0.
Step 7: Solve the equation 16 - 8k = 0 for k.
Step 8: Rearrange the equation to find k: 8k = 16.
Step 9: Divide both sides by 8 to get k = 2.
Discriminant of a Quadratic Equation – The discriminant (b^2 - 4ac) determines the nature of the roots of a quadratic equation. For real and equal roots, the discriminant must be zero.
Quadratic Formula – Understanding the quadratic formula and its components (a, b, c) is essential for solving quadratic equations.
