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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Quadratic-Equations and Factors

Grade: 1400-a Lesson: S2-L1

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	The function \$f(x) = x^2 + px + q\$ has roots r1 and r2. What is the value of f(r1 + r2)?	A) 1 B) Always Zero C) 2 D) 3
2	If one root of the equation \$ax^2 + bx + c = 0\$ is double the other, what is the relationship between a, b, and c?	A) a = 2b + c B) a = b + c C) 2a = b + c D) 2a = b + 2c
3	The graph of the function \$y = ax^2 + bx + c\$ intersects the x-axis at two distinct points. What is the SIGN of the discriminant \$(b^2 - 4ac)\$?	A) Equal B) Negative C) Positive D) Can be positive or negative
4	A projectile is launched with an initial velocity "v" and experiences a constant acceleration due to gravity, g. The height of the projectile h(t) can be modeled by a quadratic equation. What does the discriminant of this equation represent in this context?	A) Time to reach maximum height B) Time to reach minimum height C) Equal height D) None of the above
5	Two quadratic equations \$ax^2 + bx + c = 0\$ and \$dx^2 + ex + f = 0\$ share a common root. What is the relationship between the coefficients?	A) ad - bc = 0 B) ad = bc C) ad + bc = 0 D) ab - cd = 1
6	Solve the quadratic equations by completing the square: \$x^2 + 6x − 7 = 0\$	A) x = 1 and x = −7 B) x = 2 and x = 7 C) x = 1 and x = 7 D) x = 3 and x = −7
7	A ball is thrown into the air with an initial velocity of 20 m/s. Its height (in meters) after t seconds is given by h(t) = \$-5t^2 + 20t + 10\$. Find: The time it takes for the ball to hit the ground	A) \$2 - sqrt 6\$ B) \$3 - sqrt 6\$ C) \$2 + sqrt 6\$ D) \$3 + sqrt 5\$
8	Solve by Completing the Square: \$2x^2 + 8x + 5 = 0\$	A) \$x = 2 ± sqrt 6 / 3\$ B) \$x = -2 ± sqrt 6 / 2\$ C) \$x = -3 ± sqrt 5 / 2\$ D) \$x = -2 ± sqrt5 / 3\$
9	Given that one root of the quadratic equation \$2x^2 + kx + 8 = 0\$ is twice the other, find the value of k.	A) k =\$−5sqrt2\$ or k = \$6sqrt2\$ B) k =\$ 6sqrt 2\$ C) k =\$−6sqrt 2\$ or k = \$6sqrt 2\$ D) k =\$−4sqrt 2\$ or k = \$6sqrt 3\$
10	For the quadratic equation \$3^2+px+q=0\$, if the sum of the squares of the roots is 20 and the product of the roots is 4, find p and q.	A) p = \$± 3sqrt 75\$and q = 13 B) p = \$± 5sqrt 76\$ and q = 12 C) p = \$± 6sqrt 7\$ and q = 14 D) p = \$± 6sqrt 7\$ and q = 12

Problem Id

Problem

Options

The function \$f(x) = x^2 + px + q\$ has roots r1 and r2. What is the value of f(r1 + r2)?

A) 1

B) Always Zero

C) 2

D) 3

If one root of the equation \$ax^2 + bx + c = 0\$ is double the other, what is the relationship between a, b, and c?

A) a = 2b + c

B) a = b + c

C) 2a = b + c

D) 2a = b + 2c

The graph of the function \$y = ax^2 + bx + c\$ intersects the x-axis at two distinct points. What is the SIGN of the discriminant \$(b^2 - 4ac)\$?

A) Equal

B) Negative

C) Positive

D) Can be positive or negative

A projectile is launched with an initial velocity "v" and experiences a constant acceleration due to gravity, g. The height of the projectile h(t) can be modeled by a quadratic equation. What does the discriminant of this equation represent in this context?

A) Time to reach maximum height

B) Time to reach minimum height

C) Equal height

D) None of the above

Two quadratic equations \$ax^2 + bx + c = 0\$ and \$dx^2 + ex + f = 0\$ share a common root. What is the relationship between the coefficients?

A) ad - bc = 0

B) ad = bc

C) ad + bc = 0

D) ab - cd = 1

Solve the quadratic equations by completing the square: \$x^2 + 6x − 7 = 0\$

A) x = 1 and x = −7

B) x = 2 and x = 7

C) x = 1 and x = 7

D) x = 3 and x = −7

A ball is thrown into the air with an initial velocity of 20 m/s. Its height (in meters) after t seconds is given by h(t) = \$-5t^2 + 20t + 10\$. Find: The time it takes for the ball to hit the ground

A) \$2 - sqrt 6\$

B) \$3 - sqrt 6\$

C) \$2 + sqrt 6\$

D) \$3 + sqrt 5\$

Solve by Completing the Square: \$2x^2 + 8x + 5 = 0\$

A) \$x = 2 ± sqrt 6 / 3\$

B) \$x = -2 ± sqrt 6 / 2\$

C) \$x = -3 ± sqrt 5 / 2\$

D) \$x = -2 ± sqrt5 / 3\$

Given that one root of the quadratic equation \$2x^2 + kx + 8 = 0\$ is twice the other, find the value of k.

A) k =\$−5sqrt2\$ or k = \$6sqrt2\$

B) k =\$ 6sqrt 2\$

C) k =\$−6sqrt 2\$ or k = \$6sqrt 2\$

D) k =\$−4sqrt 2\$ or k = \$6sqrt 3\$

For the quadratic equation \$3^2+px+q=0\$, if the sum of the squares of the roots is 20 and the product of the roots is 4, find p and q.

A) p = \$± 3sqrt 75\$and q = 13

B) p = \$± 5sqrt 76\$ and q = 12

C) p = \$± 6sqrt 7\$ and q = 14

D) p = \$± 6sqrt 7\$ and q = 12