How will the roots of x² − 2x − 3 = 0 be?
Answer and explanation
Correct answer: Two real and distinct (D=16)
For ax²+bx+c=0, the discriminant is D=b²−4ac. In x²−2x−3=0, a=1, b=−2 and c=−3. Hence D=(−2)²−4(1)(−3)=4+12=16. Since D>0, the equation has two real and distinct roots. Because 16 is also a perfect square, the roots are rational; in fact, they are x=[2±√16]/2=(2±4)/2, giving x=3 and x=−1. The question asks about their nature, so “two real and distinct” is the correct statement in option A. Option B would require D=0, option C would require D<0, and option D is misleading because there are two rational roots, not only one.
Frequently asked questions
What is the correct answer to this question?
Two real and distinct (D=16)
Why is this the correct answer?
For ax²+bx+c=0, the discriminant is D=b²−4ac. In x²−2x−3=0, a=1, b=−2 and c=−3. Hence D=(−2)²−4(1)(−3)=4+12=16. Since D>0, the equation has two real and distinct roots. Because 16 is also a perfect square, the roots are rational; in fact, they are x=[2±√16]/2=(2±4)/2, giving x=3 and x=−1. The question asks about their nature, so “two real and distinct” is the correct statement in option A. Option B would require D=0, option C would require D<0, and option D is misleading because there are two rational roots, not only one.
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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