QQuestionMathematics
QuestionMathematics
If the discriminant of a quadratic equation is 2, then the equation has _____.
If the discriminant of a quadratic equation is 4, then the equation has _____.
If the discriminant of a quadratic equation is 0, then the equation has _____.
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Answer
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Step 1
The discriminant of a quadratic equation given by $ax^2 + bx + c = 0$ is calculated by the formula $b^2 - 4ac$.
When the discriminant is 2, it means that $b^2 - 4ac = 1$. Since the discriminant is positive, the quadratic equation has two distinct real roots. However, we cannot determine the exact values of the roots with just the discriminant value.
Step 2
This is because the discriminant is a perfect square ($(2)^2 = 4$).
This indicates that the quadratic equation has two distinct real roots, and the roots are rational and opposite in sign (i.e., one root is the negative of the other).
Final Answer
1. If the discriminant of a quadratic equation is 2, then the equation has two distinct real roots. 2. If the discriminant of a quadratic equation is 4, then the equation has two distinct rational and opposite roots. 3. If the discriminant of a quadratic equation is 0, then the equation has exactly one real repeated root.
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