Question

Use the discriminant and select whether the roots of 5x2 - 4x+3 = 0 are real or non-real.

Answer 1

The roots of 5x² - 4x + 3 = 0 are non-real

Step-by-step explanation:

In the quadratic equation ax² + bx + c = 0, the discriminant is

b² - 4ac, where a , b , c are constant

• If b² - 4ac ≥ 0, then the roots of the equation are real
• If b² - 4ac < 0, then the roots of the equation are non-real

∵ The quadratic equation is 5x² - 4x + 3 = 0

∵ The general form of the quadratic equation is ax² + bx + c = 0

∴ a = 5

∴ b = -4

∴ c = 3

∵ The discriminant is b² - 4ac

- Substitute the value of a , b and c in the discriminant

∴ b² - 4ac = (-4)² - 4(5)(3)

∴ b² - 4ac = 16 - 60

∴ b² - 4ac = -44

∵ -44 < 0

∴ b² - 4ac < 0

∴ The roots of the equations are non-real

The roots of 5x² - 4x + 3 = 0 are non-real

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