For what values of k, the equation 2x2+ kx + 1 = 0 has equal roots?

1.	For what values of k, the equation 2x2+ kx + 1 = 0 has equal roots?
Answer» Correct Answer - Option 4 : ±2√2 Concept: The solution to the quadratic equation Ax2 + Bx + C = 0 is given by: \(x = {-B \pm \sqrt{B^2-4AC} \over 2A}\) If B² - 4AC ≥ 0, the roots are real. If B2 - 4AC = 0, the roots are real and equal. If B2 - 4AC < 0, the roots will be complex and conjugates of each other. The quantity B2 - 4AC is also called the determinant. Calculation: Comparing the given equation 2x2 + kx + 1 = 0 with the general equation Ax2 + Bx + C = 0, we can say that: A = 2, B = k and C = 1. We know that for the roots to be equal, the discriminant of the quadratic equation must be equal to 0. ∴ B2 - 4AC = 0 k2 - 4(2)(1) = 0 k2 = 8 k = ±√8 k = ±2√2. The sum of both the roots of the quadratic equation Ax2 + Bx + C = 0 is \(\rm -\frac{B}{A}\) and the product of the roots is \(\rm \frac{C}{A}\). The graph of a quadratic polynomial is a parabola.

Answer» Correct Answer - Option 4 : ±2√2

Concept:

The solution to the quadratic equation Ax2 + Bx + C = 0 is given by:

\(x = {-B \pm \sqrt{B^2-4AC} \over 2A}\)

Calculation:

Comparing the given equation 2x2 + kx + 1 = 0 with the general equation Ax2 + Bx + C = 0, we can say that:

A = 2, B = k and C = 1.

We know that for the roots to be equal, the discriminant of the quadratic equation must be equal to 0.

∴ B2 - 4AC = 0

k2 - 4(2)(1) = 0

k2 = 8

k = ±√8

k = ±2√2.

The sum of both the roots of the quadratic equation Ax2 + Bx + C = 0 is \(\rm -\frac{B}{A}\) and the product of the roots is \(\rm \frac{C}{A}\).
The graph of a quadratic polynomial is a parabola.

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