The roots of the quadratic equation 2x² + 3x - 20 = 0 are:

Given:

Quadratic equation: 2x² + 3x - 20 = 0

Formula used:

Quadratic formula: x = \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

For a quadratic equation ax² + bx + c = 0

Calculations:

Comparing 2x² + 3x - 20 = 0 with ax² + bx + c = 0, we have:

a = 2

b = 3

c = -20

Substitute these values into the quadratic formula:

⇒ x = \(\frac{-3 \pm \sqrt{3^2 - 4 \times 2 \times (-20)}}{2 \times 2}\)

⇒ x = \(\frac{-3 \pm \sqrt{9 - (-160)}}{4}\)

⇒ x = \(\frac{-3 \pm \sqrt{9 + 160}}{4}\)

⇒ x = \(\frac{-3 \pm \sqrt{169}}{4}\)

⇒ x = \(\frac{-3 \pm 13}{4}\)

Two possible roots:

x₁ = \(\frac{-3 + 13}{4}\)

⇒ x₁ = \(\frac{10}{4}\)

⇒ x₁ = \(\frac{5}{2}\)

x₂ = \(\frac{-3 - 13}{4}\)

⇒ x₂ = \(\frac{-16}{4}\)

⇒ x₂ = -4

∴ The roots of the quadratic equation 2x² + 3x - 20 = 0 are \(\frac{5}{2}\) and -4.