**1.** What is the factorization of the quadratic equation 2x^{2} + 7x + 6?

a) (x + 1) (2x + 3)

b) (2x + 1) (x + 3)

c) (x + 2) (2x + 3)

d) (2x + 2) (x + 3)

**Answer:** c) (x + 2) (2x + 3)

**Explanation****: **The factors are obtained by finding two numbers whose product is equal to the product of the coefficient of x^2 and the constant term, and whose sum is equal to the coefficient of x.

2x^{2} + 7x + 6

2x^{2} + 3x + 4x + 6

x (2x + 3) + 2(2x + 3)

(x + 2) (2x + 3)

**2.** What is the factorization of the quadratic equation 4y^{2} – 12y + 9?

a) (2y – 3) (2y – 3)

b) (2y – 3)^{2}c) (2y – 3) (2y + 3)

d) (2y + 3)^{2}

**Answer:** b) (2y – 3)^{2}

**Explanation**: The equation is a perfect square trinomial, Hence

4y^{2} – 12y + 9 = (2y)^{2} – 2 x 2y x 3 + 3²

Since (a – b)^{2} = a² - 2 x a x b + b²

= (2y – 3)^{2}

**3.** What are the roots of the quadratic equation 2x^{2} + 3x – 5 = 0 using the quadratic formula?

a) x = 1 and -5/2

b) x = (3 ± √ (29)) / 4

c) x = (-3 ± √ (29)) / 2

d) x = -3/2 and 2 and

**Answer:** a) x = 1 and -5/2

**Explanation**: By substituting the values of a, b, and c into the quadratic formula, we can calculate the roots of the equation.

X = [(-3) ± √(9 + 40)]/4

x = [ -3 ± √ 49] / 4

x = [ -3 ± 7] / 4

x = 1 and -5/2

**4.** What is the discriminant of the quadratic equation 3x^{2} – 5x + 2 = 0?

a) 1

b) -1

c) 0

d) 9

**Answer:** c) 0

**Explanation**: The discriminant is calculated as b^{2} – 4ac. If the discriminant is equal to zero, it indicates that the equation has two identical roots.

B^{2} – 4ac = 25 – 4 x 3 x 2

= 25 – 24 = 1

**5.** Given equations (I) and (II), solve both equations, comparing them and select the appropriate answer from the provided options.

I) x^{2} = 49

II) y^{2} + 15y + 56 = 0

a) x > y

b) x < y

c) x ≥ y

d) x ≤ y

**Answer:** c) x ≥ y

**Explanation**: The factor of x^{2} = 49 are ± 7 and factors of y^{2} + 15y + 56 = 0 are -7 and -8. Therefore, the appropriate answer is x ≥ y.

**1.** What is the standard form of a quadratic equation?

a) ax^{2} + bx + c = 0

b) ax^{2} + c = bx

c) ax + bx^{2} + c = 0

d) a + bx^{2} + cx = 0

**Answer:** a) ax^{2} + bx + c = 0.

**2.** How many solutions does a quadratic equation have?

a) One

b) Two

c) Three

d) Four

**Answer:** b) Two.

**3.** What is the nature of the roots of a quadratic equation x² - 20x +91?

a) Real and equal

b) Real and distinct

c) Imaginary roots

d) Complex roots

**Answer:** b) Real and distinct

**4.** What is the factorization of the quadratic equation 5x^{2} + 4x - 1?

a) (5x - 1) (x + 1)

b) (5x + 1) (x - 1)

c) (5x - 1) (x - 1)

d) (5x + 1) (x + 1)

**Answer:** a) (5x - 1) (x + 1)

**5. **What is the factorization of the quadratic equation x^{2} - 2x - 3?

a) (x - 3) (x - 1)

b) (x + 3) (x + 1)

c) (x - 3) (x + 1)

d) (x + 3) (x - 1)

**Answer:** c) (x - 3) (x + 1)

**6.** What is the factorization of the quadratic equation 3x^{2} - 10x + 4?

a) (3x - 2) (x - 2)

b) (3x + 2) (x + 2)

c) (3x - 4) (x + 1)

d) (3x + 4) (x - 1)

**Answer:** a) (3x - 2) (x - 2)

**7.** What is the factorization of the quadratic equation x^{2} - 7x + 12?

a) (x - 3) (x - 4)

b)(x + 3) (x + 4)

c)(x - 3) (x + 4)

d)(x + 3) (x - 4)

**Answer**: a) (x - 3) (x - 4)

**8**. What is the factorization of the quadratic equation 2x^{2} + x - 3?

a) (2x + 3) (x - 1)

b) (2x - 3) (x + 1)

c) (2x + 1) (x - 3)

d) (2x - 1) (x + 3)

**Answer:** a) (2x + 3) (x - 1)

**9. **What is the factorization of the quadratic expression 25x^{2} - 20x + 4 using the completing square method?

a) (5x - 2) (5x - 2)

b) (5x + 2) (5x + 2)

c) (5x - 4) (5x - 4)

d) (5x - 6) (5x - 6)

**Answer: **a) (5x - 2) (5x - 2)

**10.** Given equations (I) and (II), solve both equations, comparing them and select the appropriate answer from the provided options.

(I) 2x - 5 = 13

(II) 3y + 7 = -2y + 1

a) x > y

b) x < y

c) x ≥ y

d) x ≤ y

**Answer:** a) x > y

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