Polynomials

If the HCF of (x2 + x - 12) and (2x2 - kx - 9) is (x - k), then what is the value of k?

1. 2
2. 3
3. 6
4. 5

Answer: (b) 3

Factorise the given expression: a3(b - c) + b3(c - a) + c3(a - b)

1. (a + b + c)(a - b)(b - c)(c - a)
2. - (a - b - c)(a + b)(b + c)(c + a)
3. (a - b)(b - c)(c - a)
4. (a + b + c)(a - b - c)2

Answer: (a) (a + b + c)(a - b)(b - c)(c - a)

What must be subtracted from x3 - 6x2 - 15x + 80 so that the result is exactly divisible by x2 + x - 12?

1. 4x + 8
2. 2x + 8
3. 2x + 5
4. 4x - 4

Answer: (d) 4x - 4

If a + b + c = 0, then what is the value of a4 + b4 + c4 - 2a2b2 - 2b2c2 - 2c2a2?

1. 0
2. 1
3. -1
4. 2

Answer: (a) 0

f(x) = x3 + x2 - 10x + 8, where x belongs to R. Which one of the graph is correct?

Answer: (c)

Let Sn = n2 + 20n + 12, where n is a positive integer. What is the sum of all possible values of n for which Sn is a perfect square?

1. 16
2. 10
3. 15
4. 25

Answer: (a) 16

If 'α' and 'β' are the roots of the equation 2x2 - 4x + 1 = 0, then find the value of the given expression.

1. 15
2. 12
3. 10
4. 11

Answer: (b) 12

Let a, b, c be such that a + b + c = 0 and P = a2/(2a2 + bc) + b2/(2b2 + ac) + c2/(2c2 + ab) is defined. What is the value of P?

1. 5
2. 0
3. 1
4. 10

Answer: (c) 1

If the roots of the equation (1 - q + p2/2)x2 + p(1 + q)x + q (q - 1) + p2/2 = 0 are equal, then what is the value of p2?

1. 3q2
2. 4(q + 1)
3. 4q
4. 4

Answer: (c) 4q

Read the passage and answer the following question: A group of school friends went on an expedition to see caves. One person remarked that the entrance of the caves resembles a parabola and can be represented by a quadratic polynomial f(x) = ax2 + bx + c, a ≠ 0, where a, b and c are real numbers. If one zero of the polynomial f(x) = 5x2 + 13x + m is the reciprocal of the other, then find the value of m.

1. 4
2. 7
3. 8
4. 5

Answer: (d) 5