Choose the best description of the roots of the equation 3x2 - 4x + 5 = 0.
Double root
Real and rational roots
Real and irrational roots
Imaginary roots

Solution:

The standard form of the quadratic equation ax² + bx + c = 0 and the formula used is

x = [-b ± √(b² - 4ac)]/ 2a

It is given that

3x² - 4x + 5 = 0

Here a = 3, b = -4 and c = 5

Substituting these values in the formula

x = [-(-4) ± √((-4)² - 4 × 3 × 5)]/ (2 × 3)

By further simplification

x = [4 ± √(16 - 60)]/6

x = [4 ± √-44]/ 6

So we get,

x = [4 ± 2√-11]/ 6

x = [2 ± i √11]/ 3

Also the discriminant is b² - 4ac = -44 < 0. Thus we have imaginary roots.

Therefore, the best description of the roots of the equation 3x² - 4x + 5 = 0 is imaginary roots.

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Choose the best description of the roots of the equation 3x² - 4x + 5 = 0.

Summary:

The best description of the roots of the equation 3x² - 4x + 5 = 0 is imaginary roots.