Question

When the discriminant satisfies \[D < 0\], what is the graphical behaviour of the parabola \[y = ax^{2} + bx + c\] and its number of x-intercepts?

Options

• The parabola does not meet the x-axis; 0 x-intercepts

• The parabola cuts the x-axis at exactly one point; 1 x-intercept

• The parabola cuts the x-axis at two points; 2 x-intercepts

• The parabola touches the x-axis at one point; 1 x-intercept

Answer 1

For \[D < 0\], the parabola does not meet the x-axis, giving 0 x-intercepts. Because \[b^{2} - 4ac < 0\], its square root is not real, so the quadratic equation has no real roots.