Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Worksheet: Polynomials
Polynomials Class 10 Worksheet Maths Chapter 2
Short Answer Type
Q1: If a and b are roots of the equation x2 + 7 x + 7 . Find the value of a-1 + b−1 − 2αb.
Q2: If the zeroes of the quadratic polynomial x2 + (α + 1 ) x + b are 2 and -3, then find the value of a and b.
Q.3. If a and b are zeroes of the polynomial f (x) = 2x2 − 7x + 3, find the value of α2 + b2.
Q.4: Find the zeroes of the quadratic polynomial x2 + x − 12 and verify the relationship between the zeroes and the coefficients.
Q5: If p and q are zeroes of f (x) = x2 − 5x + k, such that p − q = 1 , find the value of k.
Q6: Given that two of the zeroes of the cubic polynomial αx3 + bx2 + cx + d are 0, then find the third zero.
Q.7. If one of the zeroes of the cubic polynomial x3 + αx2 + bx + c is -1, then find the product of the other two zeroes.
Q8: If a-b, a a+b , are zeroes of x3 − 6x2 + 8x , then find the value of b
Q9: Quadratic polynomial 4x2 + 12x + 9 has zeroes as p and q . Now form a quadratic polynomial whose zeroes are p − 1 and q − 1
Long Answer Type
Q10: p and q are zeroes of the quadratic polynomial x2 − (k + 6 ) x + 2(2 k − 1) . Find the value of k if 2(p + q) = p q
Q11: Given that the zeroes of the cubic polynomial x3 − 6 x2 + 3 x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Q12: If one zero of the polynomial 2x2−5x−(2k + 1) is twice the other, find both the zeroes of the polynomial and the value of k.
Q.13: Using division show that 3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35 .
Q14: If (x - 2) and [x - 1/2 ] are the factors of the polynomials qx2 + 5x + r prove that q = r.
Q15: Find k so that the polynomial x2 + 2x + k is a factor of polynomial 2x4 + x3 - 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials.
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FAQs on Polynomials Class 10 Worksheet Maths Chapter 2
| 1. What are polynomials and how are they classified? |  |
Ans.Polynomials are algebraic expressions that consist of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. They can be classified based on their degree (the highest exponent of the variable) and the number of terms (monomial, binomial, trinomial, etc.). For example, a polynomial of degree 2 is called a quadratic polynomial.
| 2. How do you add and subtract polynomials? | |
Ans.To add or subtract polynomials, you need to combine like terms, which are terms that have the same variable raised to the same power. For instance, if you have the polynomials \(3x^2 + 2x + 1\) and \(4x^2 - 3x + 5\), you would add the coefficients of the like terms: \((3x^2 + 4x^2) + (2x - 3x) + (1 + 5) = 7x^2 - x + 6\).
| 3. What is the difference between a polynomial and a non-polynomial expression? | |
Ans.A polynomial expression has non-negative integer exponents and coefficients, while a non-polynomial expression may include negative exponents, fractions involving a variable in the denominator, or variables raised to a power that is not an integer. For example, \(2x^3 + 3x - 5\) is a polynomial, while \( \frac{1}{x} + 2\) is not a polynomial.
| 4. How do you factor polynomials? | |
Ans.Factoring polynomials involves expressing the polynomial as a product of its factors. Common methods include factoring out the greatest common factor (GCF), using the difference of squares, or applying special formulas for quadratics (like \(a^2 - b^2 = (a - b)(a + b)\)). For example, to factor \(x^2 - 9\), you would write it as \((x - 3)(x + 3)\).
| 5. What are the zeros of a polynomial and how can they be found? | |
Ans.The zeros of a polynomial are the values of the variable that make the polynomial equal to zero. They can be found using various methods, such as factoring, using the quadratic formula for quadratics, or graphing the polynomial to identify points where it crosses the x-axis. For instance, for the polynomial \(x^2 - 5x + 6\), the zeros can be found by factoring it as \((x - 2)(x - 3) = 0\), giving zeros at \(x = 2\) and \(x = 3\).
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