Question

If a, ß be the zeroes of the polynomial x2 - 8x + k
such that a2 + B2 = 40, then k = ?
O
6
O
9
O 12
O -12​

Answer 1

Step-by-step explanation:

For the general equation f(x, y) = ax2 + 2hxy + by2 + 2gx + 2fy + c = 0:

Discriminant = Δ = = abc + 2fgh - af2 - bg2 - cf2.

If Δ = 0, the equation f(x, y) = 0 represents:

If h2 - ab > 0, two distinct real lines.

If h2 - ab = 0, two parallel lines.

If h2 - ab < 0, non-real lines.

If Δ ≠ 0, the equation f(x, y) = 0 represents:

If h2 - ab > 0, a + b ≠ 0, a hyperbola.

If h2 - ab > 0, a + b = 0, a rectangular hyperbola.

If h2 - ab = 0, a parabola.

If h2 - ab < 0, h = 0, a = b, a circle.

If h2 - ab < 0, h = 0, a ≠ b, an ellipse.

Calculation:

Comparing x2 - y2 = 0 with the general equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we can say that a = 1, b = -1 and all other coefficients are 0.

Δ = abc + 2fgh - af2 - bg2 - cf2 = 0.

∴ The equation represents a pair of straight lines.