If a quadratic equation has discriminant D = −4, which conclusion is correct?
Answer and explanation
Correct answer: There are no real roots
The governing concept is the discriminant D = b² − 4ac, which determines the nature of the roots of ax² + bx + c = 0. If D is positive, the equation has two distinct real roots; if D is zero, it has two equal real roots; and if D is negative, the square root of D is not a real number. Here D = −4, so √D = √(−4) is not real. Consequently, the quadratic equation has no real roots, although it would have complex roots if complex numbers were being considered. Therefore option A is correct. Options B and C apply to D = 0 and D > 0 respectively, while option D cannot be concluded from the discriminant alone.
Frequently asked questions
What is the correct answer to this question?
There are no real roots
Why is this the correct answer?
The governing concept is the discriminant D = b² − 4ac, which determines the nature of the roots of ax² + bx + c = 0. If D is positive, the equation has two distinct real roots; if D is zero, it has two equal real roots; and if D is negative, the square root of D is not a real number. Here D = −4, so √D = √(−4) is not real. Consequently, the quadratic equation has no real roots, although it would have complex roots if complex numbers were being considered. Therefore option A is correct. Options B and C apply to D = 0 and D > 0 respectively, while option D cannot be concluded from the discriminant alone.
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.
