Worksheet: Polynomials

# Polynomials Class 10 Worksheet Maths Chapter 2

Q1: Find remainder when x3 − αx2 + 6 − α is divided by (x - a).

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

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.

The document Polynomials Class 10 Worksheet Maths Chapter 2 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

## FAQs on Polynomials Class 10 Worksheet Maths Chapter 2

 1. What is a polynomial?
Ans. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.
 2. How do I identify the degree of a polynomial?
Ans. The degree of a polynomial is determined by the term with the highest exponent. For example, if a polynomial has terms with exponents 2, 4, and 6, then its degree is 6.
 3. Can a polynomial have negative exponents?
Ans. No, a polynomial cannot have negative exponents. The exponents in a polynomial must be non-negative integers.
 4. What is the leading coefficient of a polynomial?
Ans. The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It is usually written in front of the variable with the highest exponent.
 5. How do I add or subtract polynomials?
Ans. To add or subtract polynomials, you combine like terms. Like terms have the same variables and exponents. Simply add or subtract the coefficients of the like terms while keeping the variables and exponents unchanged.

## Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

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