In a quadratic equation, if the discriminant is negative, what can be inferred a

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Question: In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?

Options:

Correct Answer: The roots are complex and conjugate.

Solution:

A negative discriminant indicates that the roots are complex and conjugate.

In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?

In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?

Step 1: Understand what a quadratic equation is. It is usually in the form ax^2 + bx + c = 0.
Step 2: Identify the discriminant in a quadratic equation. The discriminant is given by the formula D = b^2 - 4ac.
Step 3: Determine what it means for the discriminant to be negative. A negative value for D means that b^2 is less than 4ac.
Step 4: Recall the implications of the discriminant on the roots of the equation. If D is negative, the equation does not have real roots.
Step 5: Conclude that the roots must be complex numbers. Complex roots come in pairs known as conjugates, which means if one root is a + bi, the other is a - bi.

Discriminant of a Quadratic Equation – The discriminant (D) is calculated as D = b^2 - 4ac. It determines the nature of the roots of the quadratic equation ax^2 + bx + c = 0.
Nature of Roots – If the discriminant is positive, the roots are real and distinct; if it is zero, the roots are real and equal; if it is negative, the roots are complex and conjugate.