Quiz for Quadratic Equations

Q1: The roots of the equation x² − 5x + 6 = 0 are:

A. 2 and 3 B. −2 and −3 C. 1 and 6 D. 5 and 6

Q2: Discriminant of the quadratic equation x² + 4x + 5 = 0 is:

A. 16 B. −4 C. −36 D. 0

Q3: If one root of x² − 7x + k = 0 is 3, find the value of k.

A. 12 B. 9 C. 21 D. 6

Q4: If α and β are the roots of the equation x² + 2x + 3 = 0, then α + β equals:

A. 2 B. −2 C. 3 D. −3

Q5: Nature of roots of x² − 4x + 4 = 0 is:

A. Real and distinct B. Imaginary C. Real and equal D. None of these

Q6: Roots of equation x² + 1 = 0 are:

A. 1, −1 B. i, −i C. 0, 1 D. None

Q7: If the roots of x² + 2x + 1 = 0 are α and β, then αβ is:

A. 0 B. 1 C. 2 D. −1

Q8: The equation x² − x − 6 = 0 has roots:

A. 3, −2 B. 2, −3 C. −3, −2 D. 1, 6

Q9: If the sum and product of roots of a quadratic equation are 5 and 6 respectively, the equation is:

A. x² − 5x + 6 = 0 B. x² + 5x + 6 = 0 C. x² − 6x + 5 = 0 D. x² + 6x + 5 = 0

Q10: Which of the following is not a quadratic equation?

A. x² + x + 1 = 0 B. x² − 4 = 0 C. x³ + x + 1 = 0 D. 2x² + 3 = 0

Q11: If a quadratic equation has imaginary roots, then discriminant is:

A. Positive B. Negative C. Zero D. Non-negative

Q12: The graph of a quadratic function is:

A. A line B. A circle C. A parabola D. An ellipse

Q13: Minimum value of y = x² + 4x + 5 is:

A. 1 B. 5 C. −1 D. −5

Q14: If the roots of a quadratic equation are equal, then discriminant is:

A. Zero B. Positive C. Negative D. Imaginary

Q15: Which quadratic equation has roots 4 and 5?

A. x² − 9x + 20 = 0 B. x² + 9x + 20 = 0 C. x² − 1x + 9 = 0 D. x² − 4x + 5 = 0

Q16: What is the value of k if x² − 2x + k = 0 has equal roots?

A. 0 B. 1 C. 2 D. 4

Q17: If x = −1 is a root of x² + 3x + k = 0, then value of k is:

A. −4 B. −2 C. 4 D. 2

Q18: Quadratic formula is used to find:

A. Roots of a linear equation B. Roots of a quadratic equation C. Sum of series D. Limits

Q19: Which of these is always true for quadratic equations?

A. They always have real roots B. They have exactly one root C. They have at most two roots D. They have infinite solutions

Q20: If roots are reciprocal, then the product of roots is:

A. 1 B. −1 C. 0 D. 2

Q21: If x² − 4x + 3 = 0, then the larger root is:

A. 1 B. 2 C. 3 D. 4