In a quadratic equation, the expression b^2 - 4ac is called the ____.

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Multiple Choice

In a quadratic equation, the expression b^2 - 4ac is called the ____.

Explanation:
The discriminant tells us how many and what kind of roots a quadratic has. In the standard form ax^2 + bx + c = 0, the expression under the square root in the quadratic formula is b^2 - 4ac. This quantity is called the discriminant. It controls the nature of the roots: if it’s positive, there are two distinct real roots; if zero, there is one real repeated root; if negative, the roots are not real (they are complex). For example, with a = 1, b = 3, c = 2, the discriminant is 9 - 8 = 1, giving two real solutions. With a = 1, b = 2, c = 1, it’s 4 - 4 = 0, giving one real solution. With a = 1, b = 0, c = 1, it’s 0 - 4 = -4, giving nonreal roots.

The discriminant tells us how many and what kind of roots a quadratic has. In the standard form ax^2 + bx + c = 0, the expression under the square root in the quadratic formula is b^2 - 4ac. This quantity is called the discriminant. It controls the nature of the roots: if it’s positive, there are two distinct real roots; if zero, there is one real repeated root; if negative, the roots are not real (they are complex). For example, with a = 1, b = 3, c = 2, the discriminant is 9 - 8 = 1, giving two real solutions. With a = 1, b = 2, c = 1, it’s 4 - 4 = 0, giving one real solution. With a = 1, b = 0, c = 1, it’s 0 - 4 = -4, giving nonreal roots.

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