Which of the following quadratic equations has two real and distinct roots?
Answer and explanation
Correct answer: \(x^2-11x+18=0\)
For a quadratic equation \(ax^2+bx+c=0\), the nature of the roots is determined by the discriminant \(\Delta=b^2-4ac\). In option A, \(a=1, b=-11, c=18\), so \(\Delta=(-11)^2-4(1)(18)=49>0\). Hence, it has two real and distinct roots, namely \(2\) and \(9\). Options B and D have \(\Delta=0\), so they have equal real roots, whereas option C has \(\Delta<0\), so it has no real roots. Exam tip: \(\Delta>0\) always indicates two distinct real roots.
Frequently asked questions
What is the correct answer to this question?
\(x^2-11x+18=0\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the nature of the roots is determined by the discriminant \(\Delta=b^2-4ac\). In option A, \(a=1, b=-11, c=18\), so \(\Delta=(-11)^2-4(1)(18)=49>0\). Hence, it has two real and distinct roots, namely \(2\) and \(9\). Options B and D have \(\Delta=0\), so they have equal real roots, whereas option C has \(\Delta<0\), so it has no real roots. Exam tip: \(\Delta>0\) always indicates two distinct 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.
