Which statement correctly describes the nature of the roots of \(x^2+12x+36=0\)?
Answer and explanation
Correct answer: It has equal real roots
Here, \(a=1, b=12, c=36\). The discriminant is \(D=b^2-4ac=12^2-4(1)(36)=0\), so the two roots are real and equal. In fact, \(x^2+12x+36=(x+6)^2\), giving both roots as \(x=-6\). Therefore, option C is incorrect because the roots are not distinct. Exam tip: For a quadratic equation, \(D=0\) indicates equal real roots.
Frequently asked questions
What is the correct answer to this question?
It has equal real roots
Why is this the correct answer?
Here, \(a=1, b=12, c=36\). The discriminant is \(D=b^2-4ac=12^2-4(1)(36)=0\), so the two roots are real and equal. In fact, \(x^2+12x+36=(x+6)^2\), giving both roots as \(x=-6\). Therefore, option C is incorrect because the roots are not distinct. Exam tip: For a quadratic equation, \(D=0\) indicates equal 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.
