If the discriminant of a quadratic equation is \(D=-(b+3)^2\), when will its roots be real and equal?
Answer and explanation
Correct answer: \(b=-3\)
The roots of a quadratic equation are real and equal only when its discriminant is \(D=0\). Thus, \(-(b+3)^2=0\), which gives \((b+3)^2=0\) and hence \(b=-3\). Therefore, option A is correct. Exam tip: the negative of a real square can be zero only when the quantity being squared is zero.
Frequently asked questions
What is the correct answer to this question?
\(b=-3\)
Why is this the correct answer?
The roots of a quadratic equation are real and equal only when its discriminant is \(D=0\). Thus, \(-(b+3)^2=0\), which gives \((b+3)^2=0\) and hence \(b=-3\). Therefore, option A is correct. Exam tip: the negative of a real square can be zero only when the quantity being squared is zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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