If the quadratic equation \(x^2-4x+(m+4)=0\) has no real roots, which condition on \(m\) is correct?
Answer and explanation
Correct answer: \(m>0\)
A quadratic equation has no real roots when its discriminant satisfies \(D<0\). Here, \(a=1\), \(b=-4\), and \(c=m+4\), so \(D=b^2-4ac=16-4(m+4)=-4m\). Thus, \(-4m<0\), which gives \(m>0\). If \(m=0\), then \(D=0\), giving two equal real roots; therefore, option C is incorrect. Exam tip: For questions about the nature of roots, first determine the sign of the discriminant.
Frequently asked questions
What is the correct answer to this question?
\(m>0\)
Why is this the correct answer?
A quadratic equation has no real roots when its discriminant satisfies \(D<0\). Here, \(a=1\), \(b=-4\), and \(c=m+4\), so \(D=b^2-4ac=16-4(m+4)=-4m\). Thus, \(-4m<0\), which gives \(m>0\). If \(m=0\), then \(D=0\), giving two equal real roots; therefore, option C is incorrect. Exam tip: For questions about the nature of roots, first determine the sign of the discriminant.
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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