Kerala SSLC · Mathematics · Class 10

Polynomials: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Polynomials” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.

1. Q1.What is the sum of the zeroes of the polynomial 2x^2 - 8x + 6?

   • A)4
   • B)-4
   • C)3
   • D)-3

   Answer: A) 4

   For a quadratic polynomial ax^2 + bx + c, the sum of zeroes is given by -b/a. Here, -(-8)/2 equals 4.

2. Q2.Which polynomial has zeroes whose sum is 5 and product is 6?

   • A)x^2 - 5x + 6
   • B)x^2 + 5x + 6
   • C)x^2 - 5x - 6
   • D)x^2 + 5x - 6

   Answer: A) x^2 - 5x + 6

   The standard form is x^2 - (sum)x + (product). Substituting sum = 5 and product = 6 yields x^2 - 5x + 6.

3. Q3.According to the Division Algorithm for polynomials, what is the condition for the remainder r(x)?

   • A)r(x) = 0
   • B)Degree of r(x) < Degree of g(x)
   • C)Degree of r(x) = Degree of g(x)
   • D)r(x) must be constant

   Answer: B) Degree of r(x) < Degree of g(x)

   The Division Algorithm states p(x) = g(x)q(x) + r(x), where r(x) is either zero or its degree is strictly less than the divisor g(x).

4. Q4.If one zero of x^2 - 3x - 10 is 5, what is the other zero?

   • A)-2
   • B)2
   • C)-5
   • D)10

   Answer: A) -2

   The product of zeroes is c/a, which is -10. Since one zero is 5, the other must be -10/5, which equals -2.

5. Q5.The graph of a quadratic polynomial intersects the x-axis at two distinct points. How many zeroes does it have?

   • A)0
   • B)1
   • C)2
   • D)3

   Answer: C) 2

   Each point where the graph intersects the x-axis corresponds to a real zero. Therefore, two intersections indicate two distinct real zeroes.

6. Q6.If the sum of the zeroes of x^2 - kx + 12 is 7, what is the value of k?

   • A)7
   • B)-7
   • C)12
   • D)-12

   Answer: A) 7

   The sum of zeroes is -b/a. Here, -(-k)/1 equals k. Since the sum is given as 7, k must be 7.

7. Q7.If the zeroes of a quadratic polynomial are reciprocals of each other, which relationship holds true?

   • A)a = b
   • B)b = c
   • C)a = c
   • D)a = -c

   Answer: C) a = c

   The product of zeroes is c/a. If zeroes are reciprocals, their product is 1, implying c/a = 1, so a = c.

8. Q8.When a cubic polynomial is divided by a linear polynomial, what is the degree of the quotient?

   • A)0
   • B)1
   • C)2
   • D)3

   Answer: C) 2

   The degree of the quotient is found by subtracting the degree of the divisor from the dividend. Thus, 3 - 1 equals 2.

9. Q9.What is the product of the zeroes of 3x^2 - 12?

   • A)-12
   • B)12
   • C)-4
   • D)4

   Answer: C) -4

   The product of zeroes is calculated as c/a. Here, c is -12 and a is 3, so -12 divided by 3 equals -4.

10. Q10.If alpha and beta are zeroes of x^2 + 4x + 2, find the value of alpha^2 + beta^2.

    • A)12
    • B)16
    • C)20
    • D)8

    Answer: A) 12

    Using the identity alpha^2 + beta^2 = (sum)^2 - 2(product), we get (-4)^2 - 2(2) = 16 - 4 = 12.

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