Theory of Equations MCQ

Class 12 TN State Board | Mathematics

1. What is the degree of the equation 3x^2 – 2x + 1 = 0?
   A) 2
   B) 3
   C) 1
   D) 0
2. Which of the following is not a quadratic equation?
   A) 2x^2 + 3x + 1 = 0
   B) x^3 – 4x^2 + 5x – 2 = 0
   C) 4x^2 – 7x + 3 = 0
   D) x^2 + 2x + 2 = 0
3. If a quadratic equation has no real roots, what can be said about its discriminant (D)?
   A) D < 0 B) D > 0
   C) D = 0
   D) D can be positive or negative
4. How many real roots does the equation x^2 + 4x + 4 = 0 have?
   A) 0
   B) 1
   C) 2
   D) Infinite
5. The sum of the roots of the equation 2x^2 – 5x + 3 = 0 is:
   A) 2
   B) 3/2
   C) 5/2
   D) 5
6. If one root of the equation x^2 – 6x + k = 0 is 2, what is the other root?
   A) -2
   B) 3
   C) 4
   D) 6
7. Which of the following equations represents a linear equation?
   A) x^2 – 5x + 6 = 0
   B) 2x^2 + 3x – 1 = 0
   C) 3x – 4 = 0
   D) x^3 + 2x^2 + x – 3 = 0
8. The product of the roots of the equation x^2 – 9x + 20 = 0 is:
   A) 9
   B) 20
   C) -9
   D) 2
9. Which of the following equations has roots that are equal and real?
   A) x^2 – 4x + 4 = 0
   B) x^2 + 2x + 2 = 0
   C) x^2 – 5x + 7 = 0
   D) x^2 – 3x + 5 = 0
10. What is the value of the discriminant (D) for a perfect square trinomial?
    A) D > 0
    B) D = 0
    C) D < 0
    D) D can be positive or negative
11. If the roots of a quadratic equation are real and equal, what can be said about the discriminant (D)?
    A) D < 0 B) D > 0
    C) D = 0
    D) D can be positive or negative
12. If the equation x^2 – 7x + a = 0 has equal roots, what is the value of ‘a’?
    A) 49
    B) 24
    C) 9
    D) 7
13. Which of the following equations represents a quadratic equation in standard form?
    A) 3x^2 + 2x + 1 = 0
    B) 2x^2 – 5x + 3 = 0
    C) x^2 – 4 = 0
    D) x^2 – 3x = 7
14. If a quadratic equation has no real roots, how many complex roots does it have?
    A) 0
    B) 1
    C) 2
    D) 3
15. What is the sum of the squares of the roots of the equation x^2 – 8x + 12 = 0?
    A) 8
    B) 12
    C) 16
    D) 64
16. Which of the following equations represents a quadratic equation with no real roots?
    A) x^2 + 4x + 4 = 0
    B) x^2 – 6x + 9 = 0
    C) x^2 + 3x + 2 = 0
    D) x^2 – 2x + 5 = 0
17. What is the value of ‘a’ in the equation ax^2 + 6x – 9 = 0 if it has two equal roots?
    A) 3
    B) 6
    C) 9
    D) 2
18. Which of the following equations has roots that are reciprocal of each other?
    A) x^2 – 5x + 6 = 0
    B) x^2 + 3x + 2 = 0
    C) x^2 – 4x + 1 = 0
    D) x^2 – 6x + 9 = 0
19. If the roots of the equation x^2 + px + 4 = 0 are equal, what is the value of ‘p’?
    A) 4
    B) -4
    C) 2
    D) -2
20. Which of the following represents the sum of the roots of the equation ax^2 + bx + c = 0?
    A) -b/a
    B) -c/a
    C) b/a
    D) c/a

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