What is the discriminant of the quadratic equation x² – 4x + 2 = 0?

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The discriminant is a crucial part of solving quadratic equations, given by the formula: D = b² – 4ac, where ax² + bx + c = 0. For the quadratic equation in question, x² – 4x + 2 = 0, the coefficients are:

  • a = 1
  • b = -4
  • c = 2

Now, substituting these values into the formula gives:

D = (-4)² - 4(1)(2) = 16 - 8 = 8

Thus, the discriminant D equals 8.

This positive discriminant indicates that there are two distinct real roots for the quadratic equation. In fact, we can calculate these roots using the quadratic formula:

x = \frac{-b \pm \sqrt{D}}{2a}

Substituting the known values into the formula:

x = \frac{-(-4) \pm \sqrt{8}}{2(1)} = \frac{4 \pm 2\sqrt{2}}{2} = 2 \pm \sqrt{2}

The roots are thus 2 + √2 and 2 – √2.

In summary, the discriminant of the quadratic equation x² – 4x + 2 = 0 is 8, which confirms the presence of two distinct real roots.

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