# Class 8 Maths Chapter 2 Question Answers - Polynomials

Q 1. How many zeroes can the polynomial 2x- 3x + 4 have?

It is a quadratic polynomial i.e. the degree of 2x- 3x + 4 is 2.
∴ It can have two zeroes at the most.

Q 2. The graph of y = p (x) is shown in the figure below. How many zeroes does p (x) have?

Since the curve (graph) of p (x) is intersecting the x-axis at three points,
∴ y = p (x) has 3 zeroes.

Q 3. What is the value of p (x) = x2 - 3x - 4 at x = 2?

Given,
p(x) = x2 - 3x - 4
⇒ p(2) = (2)2 - 3 (2) - 4
⇒ 4 - 6 - 4 = - 6

Q 4. What is the value of p (x) = x2 - 3x - 4 at x = - 1?

We have,
p(x) = x- 3x - 4
⇒ p (- 1) = (- 1)- {3 (- 1)} - 4
⇒ 1 + 3 - 4 = 0

Q 5. What is the zero of 2x + 3?

Since,
The zero of a linear polynomial =
∴ The zero of 2x + 3 = -3/2

Q 6. The Coefficient of x and the constant term in a linear polynomial are 5 and - 3 respectively. Find its zero.

Since,
The zero of a linear polynomial
∴ The zero of the given linear polynomial

Q 7. The graph of a quadratic polynomial x2 - 3x - 4 is a parabola. Determine the opening of the parabola.

In x2 - 3x - 4, the Coefficient of x2 is 1 and 1 > 0
∴ The parabola opens upwards.

Q 8. Find the sum of the zeroes of the polynomial 2x- 8x + 6.
p (x) = x2 - 3x - 4

p (x) = 2x2 - 8x + 6
∴ a = 2, b = - 8 and c = 6
⇒ Sum of the zeroes = -b/a
⇒ -(-8)/(2) = 4

Q 9. Find the product of zeroes of the quadratic polynomial 3x2 + 5x - 2.

Here, a = 3, b = 5 and c = - 2
As, Product of the zeroes = c/a
⇒ Product of the zeroes of 3x2 + 5x - 2 = -2/3

Q 10. If a fifth degree polynomial is divided by a quadratic polynomial, write the possible degree of the quotient.

∵ Degree of the dividend p(x) = 5
Degree of the divisor f(x) = 2
∴ Degree of the quotient q(x) = Degree of p(x) - Degree of f(x) = 5 - 2 = 3

Q 11. Graph of a linear polynomial is a straight line. If the points (0, 4), (1, 2) and (2, 0) lie on this graph, write the zero of the polynomial.

y = p (x) has its zero at a point where y = 0
In the figure, y = 0 at (2, 0).
∴ 2 is the zero of p (x).

Q 12. For what value of k, (- 4) is a zero of the polynomial x2 - x - (2k + 2)?

Since, (- 4) is the zero of p (x)
⇒ p (- 4) = (- 4)2 - (- 4) - (2k + 2) = 0
⇒ 16 + 4 = 2k + 2
⇒ 20 - 2 = 2k
⇒ 18= 2k
⇒ k = 18/2 = 9
Thus, the required value of k = 9.

Q 13. For what value of p, (- 4) is a zero of the polynomial x2 - 2x - (7p + 3)?

We have
∵ p (x) = x2 - 2x - (7p + 3)
p (- 4) = (- 4)2 - 2 (- 4) - (7p + 3)
Since - 4 is a zero of p (x),
∴ (- 4)2 - 2 (- 4) - (7p + 3) = 0
⇒ 16 + 8 = 7p + 3
⇒ 24 - 3 = 7p
⇒ 7p = 21
⇒ p = 21/7= 3
Thus, the required value of p is 3.

Q 14. The sum and product of the zeroes of a quadratic polynomial are and - 3 respectively. What is the quadratic polynomial?

For a quadratic polynomial, we have
Sum of zeroes = -1/2

Product of the zeroes = -3
Since general equation of the quadratic polynomial
= x2 - [Sum of the roots] x + [Product of the roots]

Q 15. The graph of y = f (x) is given in the figure, find the number of zeroes of f (x).

From the figure (graph), it is evident that y = f (x) intersects the x-axis at two distinct points A and B.
∴ Number of zeroes of f (x) = 2.

Q 16. In the adjoining figure the graph of a polynomial p (x) is given. Find the zeroes of the polynomial.

From the graph, it is evident that the graph of the given polynomial intersects the x-axis at - 1 and - 3.
∴ The zeroes of the polynomial are - 1 and - 3.

Q 17. If 1 is a zero of the polynomial p (x) = ax2 - 3 (a - 1) x - 1, then find the value of a.

Here, p (x) = ax2 - 3(a - 1)x - 1
∴ p(1) = a(1)- 3(a - 1) × 1 - 1
= a - 3a + 3 - 1
= - 2a + 2
∵ 1 is a zero of p (x);
∴ p (1) = 0
⇒ - 2a + 2 = 0 ⇒ a = 1

Q 18. If (x + a) is a factor of 2x2 + 2ax + 5x + 10 find a.

Here, p(x) = 2x+ 2ax + 5x + 10
∵ (x + a) is a factor of p(x)
∴ - a is a zero of p(x)
⇒ p (- a) = 0
⇒ 2 (- a)2 + 2a (- a) + 5 (- a) + 10 = 0
⇒ 2a2 - 2a2 - 5a + 10 = 0
⇒ a = 10/5 = 2
Thus, the required value of a = 2.

Q 19. Write the zeroes of the polynomial x2 + 2x + 1.

We have,
p (x) = x2 + 2x + 1
= (x + 1)2
If p (x) = 0 then (x + 1)2 = 0
⇒ x = - 1
Thus, the zero of the polynomial p (x) is - 1.

Q 20. Write the zeroes of the polynomial x2 - x - 6.

We have,
p (x) = x2 - x - 6
= x2 - 3x + 2x - 6
⇒ x (x - 3) + 2 (x - 3)
⇒ (x - 3) (x + 2)
For p (x) = 0
⇒ (x - 3) (x + 2) = 0
∴ x = 3 and x = - 2

Q 21. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and - 2 respectively.

A quadratic polynomial is given by
x2 - [Sum of the zeroes] x + [Product of zeroes]
But, Sum of zeroes = 3
Product of zeroes = - 2
= x- 3x + (- 2)
= x2 - 3x - 2

Q 22. Write the number of zeroes of the polynomial y = f (x) whose graph is given in the figure.

Since, curve (graph) of y = f (x) intersects the x-axis at three points,
∴ y = f (x) has three zeroes.

Q 23. The graph of y = f (x) is given in figure. How many zeroes are there of f (x)?

The graph of y = f (x) does not intersect the x-axis.
∴ The number of zeroes of f (x) is 0.

Q 24. The graph of y = f (x) is given in the figure. What is the number of zeroes of f (x)?

Since, the graph of y = f (x) intersects the x-axis at three distinct points,
∴ y = f (x) has 3 zeroes.

Q 25. What is the number of zeroes of the polynomial y = p (x)?

Since, the graph passes through origin(0,0) which means on putting x = 0, we get y = 0.
Therefore, (0,0) is the only root of this equation.

The document Class 8 Maths Chapter 2 Question Answers - Polynomials is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

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## FAQs on Class 8 Maths Chapter 2 Question Answers - Polynomials

 1. What is a polynomial?
A polynomial is a mathematical expression consisting of variables, coefficients, and exponentiation, combined using addition, subtraction, and multiplication. It can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer exponents.
 2. How do you determine the degree of a polynomial?
To determine the degree of a polynomial, you need to find the highest power of the variable in the expression. For example, if the polynomial is 3x^2 + 5x - 2, the degree is 2 because the highest power of x is 2.
 3. What is the difference between a monomial and a polynomial?
A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For instance, 3x^2 is a monomial as it has only one term, whereas 3x^2 + 5x - 2 is a polynomial since it has three terms.
 4. How do you add or subtract polynomials?
To add or subtract polynomials, you combine like terms. Like terms have the same variables raised to the same power. For example, to add 3x^2 + 5x - 2 and 2x^2 - 4x + 1, you add the coefficients of like terms: (3x^2 + 2x^2) + (5x - 4x) + (-2 + 1) = 5x^2 + x - 1.
 5. How do you multiply polynomials?
To multiply polynomials, you use the distributive property and the properties of exponents. Multiply each term of one polynomial by each term of the other polynomial, and then combine like terms. For example, to multiply (3x - 2) and (2x + 1), you would do: 3x * 2x + 3x * 1 + (-2) * 2x + (-2) * 1 = 6x^2 + 3x - 4x - 2 = 6x^2 - x - 2.

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