If the discriminant of a quadratic equation is \(D=(w+2)^2\), what must be the value of \(w\) for the equation to have equal roots?
Answer and explanation
Correct answer: \(w=-2\)
A quadratic equation has equal roots when its discriminant is \(D=0\). Thus, \((w+2)^2=0\), which gives \(w+2=0\) and hence \(w=-2\). The distractor \(w=2\) gives \(D=16\), leading to two distinct real roots, not equal roots. Exam tip: remember that \(D=0\) indicates equal roots, \(D>0\) indicates two distinct real roots, and \(D<0\) indicates no real roots.
Frequently asked questions
What is the correct answer to this question?
\(w=-2\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is \(D=0\). Thus, \((w+2)^2=0\), which gives \(w+2=0\) and hence \(w=-2\). The distractor \(w=2\) gives \(D=16\), leading to two distinct real roots, not equal roots. Exam tip: remember that \(D=0\) indicates equal roots, \(D>0\) indicates two distinct real roots, and \(D<0\) indicates no real roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
