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

Evaluate the limit using the definition of the derivative: \$lim_(h->0) (f(x +h) - f(x))/ h\$ where f(x) = \$x^2 + 3x\$.

A) 2x + 5

B) 2x + 3

C) x + 3

D) 4x + 7

If one of the zeros of the quadratic polynomial \$(k - 1)(x^2) + kx + 1\$ is -3, then the value of k is:

A) \$- 2 / 3\$

B) \$4 / 3\$

C) \$- 4 / 3\$

D) \$2 / 3\$

Find the roots of the quadratic equation:
\$ (x^2 - 25)/ (x^2 + 5x + 6) \$ = 0.

A) x = ± 4

B) x = 5

C) x = ± 5

D) x = 4

Solve the quadratic equation:
\$ (3/(x + 1)) + (2/(x + 2)) \$ = 4.

A) x = 0 and \$- 7/4\$

B) x = 11 and \$ - 4/7\$

C) x = 2 and \$7/4\$

D) x = 1 and \$ 4/7\$

Solve \$lim_(h->0) ((a + h)^2 sin(a + h) - (a^2 sina)) / h\$.

A) \$3 sin a + a^2 cos a\$

B) \$2 sin a - a^2 cos a\$

C) \$2 sin a + a^2 cos a\$

D) \$2 sin a + a^3 cos a\$

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 these.

Given f(x) is a polynomial of degree 4 such that f(1) = 10, f(2) = 20, f(3) = 30, f(4) = 40, find f(5).

A) 8

B) 24

C) 33

D) 70

Solve the equation \$(x^3 + x^2 - 20x) / (x^4 - 12x^3 + 36x^2)\$.

A) x = - 4 and x = - 4

B) x = - 5 and x = 4

C) x = - 5 and x = 5

D) x = - 5 and x = 6

Given that \$ p(x) = x^3 + ax^2 + bx + c \$ has roots 1, 2 and 3, we need to find the value of b − c.

A) 23

B) 45

C) 17

D) 20