Given the equation: $x^2 - 2x + 6 = 0$ 2.1.1 Determine the numerical value of the discriminant - NSC Technical Mathematics - Question 2 - 2022 - Paper 1

Since the discriminant $riangle = -20$ is less than zero, it indicates that the roots of the equation are non-real or imaginary roots. This means that the quadratic equation does not intersect the x-axis.

To find the value of $k$ that allows the quadratic equation to have real roots, again we calculate the discriminant:

$riangle = b^2 - 4ac$

For this equation, we have:

• $a = 1$
• $b = 2$
• $c = k$

Substituting these values, we get:

$riangle = (2)^2 - 4(1)(k)$ $riangle = 4 - 4k$

For the equation to have real roots, we require $riangle eq 0$, which leads to:

$4 - 4k \geq 0$ $4 \eq 4k$ $k \eq 1$

Thus, the numerical value of $k$ must satisfy $k \eq 1$ to ensure that the equation has real roots.