In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?
Practice Questions
1 question
Q1
In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?
The roots are real and distinct.
The roots are real and equal.
The roots are complex and conjugate.
The roots are imaginary.
A negative discriminant indicates that the roots are complex and conjugate.
Questions & Step-by-step Solutions
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Q
Q: In a quadratic equation, if the discriminant is negative, what can be inferred about the roots?
Solution: A negative discriminant indicates that the roots are complex and conjugate.
Steps: 5
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.
