In simplest radical form, what are the solutions to the quadratic equation 0 = -3x² - 4x + 5?

Solution:

It is given that,

0 = -3x² - 4x + 5

The equation for the discriminant is

Δ = b² - 4ac

Where, a = -3, b = -4, c = 5

Δ = (-4)² - (4 ×(-3)× 5)

Δ = 16 + 60

Δ = 76

Now apply square root on both side,

√Δ = √76

√Δ = √(19 × 4)

√Δ = √19 × √4

√Δ = 2√19

Then,

x₁ = (- b - √Δ)/2a

x₂ = (- b + √Δ)/2a

So,

x₁ = (- (-4) - 2√19)/(2 × (-3))

x₁ = (4 - 2√19)/-6

x₁ = -(2 - √19)/3

And,

x₂ = (- (-4) + 2√19)/(2 × (-3))

x₂ = (4 + 2√19)/-6

x₂ = -(2 + √19)/3

Therefore, the solutions to the quadratic equation are x₁ = -(2 - 2√19)/3 or x₂ = -(2 + 2√19)/3.

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In simplest radical form, what are the solutions to the quadratic equation 0 = -3x² - 4x + 5?

Summary:

In the simplest radical form, the solutions to the quadratic equation 0 = -3x² - 4x + 5 are x₁ = -(2 -√19)/3 or x₂ = -(2 +√19)/3.