Q.1 What is the standard form of a quadratic equation?
ax^2 + bx + c = 0
ax + b = 0
ax^3 + bx^2 + c = 0
a/x + b = 0
Explanation - A quadratic equation is any equation that can be written in the form ax^2 + bx + c = 0, where a ≠ 0.
Correct answer is: ax^2 + bx + c = 0
Q.2 What is the degree of a quadratic equation?
1
2
3
4
Explanation - The highest power of the variable in a quadratic equation is 2, so the degree is 2.
Correct answer is: 2
Q.3 Which of the following is a quadratic equation?
2x + 5 = 0
x^2 + 3x + 2 = 0
x^3 - 4 = 0
5x - 7 = 0
Explanation - Quadratic equations must have the highest exponent of x as 2. Only x^2 + 3x + 2 = 0 satisfies this.
Correct answer is: x^2 + 3x + 2 = 0
Q.4 In the quadratic equation ax^2 + bx + c = 0, what must be true about a?
a = 0
a ≠ 0
a > 0
a < 0
Explanation - If a = 0, the equation becomes linear, so a must not equal 0 for it to be quadratic.
Correct answer is: a ≠ 0
Q.5 Which method is NOT commonly used to solve quadratic equations?
Factoring
Quadratic formula
Completing the square
Differentiation
Explanation - Quadratic equations are solved using factoring, the quadratic formula, or completing the square. Differentiation is a calculus method, not a direct solution method.
Correct answer is: Differentiation
Q.6 If x^2 - 5x + 6 = 0, what are the solutions?
x = 2 and 3
x = -2 and -3
x = 1 and 6
x = -1 and -6
Explanation - Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Correct answer is: x = 2 and 3
Q.7 Which formula gives the roots of a quadratic equation ax^2 + bx + c = 0?
(-b ± √(b^2 - 4ac)) / 2a
(-c ± √(b^2 - 4ac)) / 2a
(-b ± √(ac - b^2)) / 2a
(b ± √(b^2 - 4ac)) / 2c
Explanation - The quadratic formula for solving ax^2 + bx + c = 0 is (-b ± √(b^2 - 4ac)) / 2a.
Correct answer is: (-b ± √(b^2 - 4ac)) / 2a
Q.8 What is the discriminant of the quadratic equation ax^2 + bx + c = 0?
b^2 - 4ac
b^2 + 4ac
2a
b^2 - 2ac
Explanation - The discriminant is b^2 - 4ac, and it helps determine the nature of roots of the quadratic equation.
Correct answer is: b^2 - 4ac
Q.9 If the discriminant of a quadratic equation is positive, what type of roots does it have?
Real and equal
Real and unequal
Imaginary
Zero
Explanation - When b^2 - 4ac > 0, the equation has two distinct real roots.
Correct answer is: Real and unequal
Q.10 If the discriminant is zero, the quadratic equation has:
Two equal real roots
Two unequal real roots
No real roots
Infinite roots
Explanation - When b^2 - 4ac = 0, the quadratic has one repeated real root (two equal roots).
Correct answer is: Two equal real roots
Q.11 If the discriminant is negative, the quadratic equation has:
Two real roots
Two imaginary roots
One root
Infinite roots
Explanation - When b^2 - 4ac < 0, the roots are non-real complex conjugates.
Correct answer is: Two imaginary roots
Q.12 Solve x^2 - 4 = 0.
x = 2 or -2
x = 4 or -4
x = 0 or 4
x = -1 or 1
Explanation - x^2 = 4 gives x = ±2.
Correct answer is: x = 2 or -2
Q.13 If (x - 1)(x - 2) = 0, what are the solutions?
x = 1 and 2
x = -1 and -2
x = 2 only
x = 1 only
Explanation - Each factor gives a solution: x = 1 or x = 2.
Correct answer is: x = 1 and 2
Q.14 Find the roots of x^2 + 5x + 6 = 0.
x = -2, -3
x = 2, 3
x = -1, -6
x = 1, 6
Explanation - Factoring: (x + 2)(x + 3) = 0, so roots are -2 and -3.
Correct answer is: x = -2, -3
Q.15 Which equation has equal roots?
x^2 + 4x + 4 = 0
x^2 + 5x + 6 = 0
x^2 - 3x + 2 = 0
x^2 - x - 6 = 0
Explanation - x^2 + 4x + 4 = (x+2)^2 has a double root at x = -2.
Correct answer is: x^2 + 4x + 4 = 0
Q.16 Solve 2x^2 - 8 = 0.
x = ±2
x = ±4
x = ±√8
x = ±√2
Explanation - 2x^2 = 8 ⇒ x^2 = 4 ⇒ x = ±2.
Correct answer is: x = ±2
Q.17 What is the sum of the roots of ax^2 + bx + c = 0?
-b/a
c/a
b/a
-c/a
Explanation - Sum of roots formula: -b/a.
Correct answer is: -b/a
Q.18 What is the product of the roots of ax^2 + bx + c = 0?
c/a
-c/a
-b/a
a/c
Explanation - Product of roots formula: c/a.
Correct answer is: c/a
Q.19 Find the discriminant of 2x^2 - 4x + 2 = 0.
0
4
8
16
Explanation - b^2 - 4ac = (-4)^2 - 4(2)(2) = 16 - 16 = 0.
Correct answer is: 0
Q.20 Solve x^2 + x - 6 = 0.
x = 2, -3
x = -2, 3
x = 1, -6
x = -1, 6
Explanation - Factoring: (x+3)(x-2) = 0 ⇒ roots are -3 and 2.
Correct answer is: x = 2, -3
Q.21 If roots of a quadratic are equal, what is true about the discriminant?
> 0
< 0
= 0
None of these
Explanation - Equal roots occur when discriminant = 0.
Correct answer is: = 0
Q.22 Solve x^2 + 4x + 4 = 0.
x = -2, -2
x = 2, 2
x = -4, 0
x = -1, -4
Explanation - x^2 + 4x + 4 = (x+2)^2 ⇒ double root at -2.
Correct answer is: x = -2, -2
Q.23 Solve x^2 + 2x + 5 = 0.
No real roots
x = -1 ± 2i
x = 1 ± 2i
x = -2 ± i
Explanation - Discriminant = 2^2 - 20 = -16 < 0 ⇒ roots are -1 ± 2i.
Correct answer is: x = -1 ± 2i
Q.24 If the roots of ax^2 + bx + c = 0 are p and q, then the equation can be written as:
a(x - p)(x - q) = 0
a(x + p)(x + q) = 0
a(x + p)(x - q) = 0
a(x - p)(x + q) = 0
Explanation - If roots are p and q, equation is a(x - p)(x - q) = 0.
Correct answer is: a(x - p)(x - q) = 0