Solve x in the given equation : \$2x^2 - 9x - 18\$ = 0

A) \$x = 3/6 \$ or x = 8

B) \$x = - 3/6 \$ or x = 6

C) \$x = 3/6 \$ or x = - 6

D) \$x = - 5/6 \$ or x = 10

Let α, β; α > β, , be the roots of the equation \$x^2 - \sqrt2x - \sqrt3 = 0\$. Let \$P_n = α^n - β^n\$, n ∈ N.
Then \$(11 \sqrt3 - 10 \sqrt2) P_10 + (11 \sqrt2 + 10) P_11 - 11 P_12\$ is equal to

A) \$15 \sqrt6 P_12\$

B) \$12 \sqrt5 P_8\$

C) \$10 \sqrt3 P_9\$

D) \$15 \sqrt3 P_9\$

Find the angle between A = (2, 0, - 2) and B = (0, 3, - 3). First, find the scalar product.

A) 50°

B) 65°

C) 55°

D) 60°

The sum of all the solutions of the equation \$(8)^2x - 16 * (8)^x + 48 = 0\$ is.

A) \$1 + log_8(6)\$

B) \$1 + log_8(7)\$

C) \$1 + log_8(9)\$

D) \$1 + log_9(5)\$

Solve the quadratic equation : \$2x^2 + 4x - 6\$ = 0.

A) x = 1 or x = - 3

B) x = - 1 or x = - 3

C) x = 1 or x = 3

D) x = 1 or x = - 4

If 2 and 6 are the roots of the equation \$ax^2 + bx + 1 = 0\$, then the quadratic equation, whose roots are \$1/2 a + b\$ and \$1/6 a + b\$, is.

A) \$x^2 + 8x + 12\$ = 0

B) \$2x^2 + 11x + 12\$ = 0

C) \$4x^2 + 14x + 12\$ = 0

D) \$x^2 + 10x + 16\$ = 0]

Let S = { x ∈ R : \$(sqrt3 + sqrt2)^x + (sqrt3 - sqrt2)^x\$ = 10}. Then the number of elements in S is.

A) 2

B) 0

C) 4

D) 1

The number of real roots of the equation \$x |x | - 5|x + 2| + 6 = 0\$, is.

A) 4

B) 3

C) 5

D) 6

Solve the quadratic equation \$x^2 + 7x + 10\$ = 0 by splitting the middle term.

A) x = 2 and x = - 5

B) x = - 2 and x = 5

C) x = - 2 and x = - 5

D) x = 2 and x = 5

Factorize \$3x^2 + 7x + 4\$ = 0.

A) \$x = 4 / 3\$ and x = 1

B) \$x = - 4 / 3\$ and x = 1

C) \$x = 4 / 3\$ and x = - 1

D) \$x = - 4 / 3\$ and x = - 1