How many real roots does the equation \(x^2+4=0\) have?
Answer and explanation
Correct answer: 0
Since \(x^2\ge 0\), we have \(x^2+4\ge 4>0\), so \(x^2+4\) can never be zero and there are no real roots. Using the quadratic discriminant: \(\Delta=b^2-4ac=0^2-4\cdot1\cdot4=-16<0\), which confirms no real solutions. Common distractor: students may think a quadratic always has two roots — that requires \(\Delta>0\). Exam tip: check \(\Delta\) or the minimum value of \(x^2\) to decide real roots quickly.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Since \(x^2\ge 0\), we have \(x^2+4\ge 4>0\), so \(x^2+4\) can never be zero and there are no real roots. Using the quadratic discriminant: \(\Delta=b^2-4ac=0^2-4\cdot1\cdot4=-16<0\), which confirms no real solutions. Common distractor: students may think a quadratic always has two roots — that requires \(\Delta>0\). Exam tip: check \(\Delta\) or the minimum value of \(x^2\) to decide real roots quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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