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## Answers

*Find the discriminant in the expression: b² - 4ac*

*From a given quadratic equation ax² + bx + c = 0, substitute the values of a, b, and c to the discriminant formula.*

*If b² - 4ac = 0, the nature of the roots is one real root of multiciplicity 2.*

*If b² - 4ac > 0 and is a perfect square; there are two distinct real roots, which are rational.*

*If b² - 4ac > 0 but NOT perfect square, there are two distinct real roots, which is irrational.*

*If b² - 4ac < 0, there is no real root.*

*Example:*

*4x² - 2x = -3*

*Re-write to:*

*4x² - 2x + 3 = 0*

*a = 4; b = -2; c = 3*

*Discriminant = b² - 4ac*

*Discriminant =(-2)² - 4 (4)(3)*

*Discriminant = 4 - 48*

*Discriminant = - 44*

*- 44 < 0 Therefore there is no real root.*