Tomorrow is my mathematices online test guys plz help me from chapter: (polynomials) class9 So can u say the important questions from this chapter plz help me. If u gave the questions that give with solutions ok...... only of 5 marks.
Answers
Answer:
Q1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
Solution:
The equation 4x2 – 3x + 7 can be written as 4x2 – 3x1 + 7x0
Since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x2 – 3x + 7 is a polynomial in one variable.
(ii) y2 + √2
Solution:
The equation y2 + can be written as y2 + y0
Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y2 + is a polynomial in one variable.
(iii) 3√t + t√2
Solution:
The equation 3 + t can be written as 3t1/2 + √2t
Though, t is the only variable in the given equation, the powers of t (i.e.,) is not a whole number. Hence, we can say that the expression 3 + t is not a polynomial in one variable.
(iv) y + 2/y
Solution:
The equation y + can be written as y+2y-1
Though, y is the only variable in the given equation, the powers of y (i.e.,-1) is not a whole number. Hence, we can say that the expression y + is not a polynomial in one variable.
(v) x10 + y3 + t50
Solution:
Here, in the equation x10 + y3 + t50
Though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression
x10 + y3 + t50. Hence, it is not a polynomial in one variable.
Q2. Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x
Solution:
The equation 2 + x2 + x can be written as 2 + (1) x2 + x
We know that, coefficient is the number which multiplies the variable.
Here, the number that multiplies the variable x2 is 1
, the coefficients of x2 in 2 + x2 + x is 1.
(ii) 2 – x2 + x3
Solution:
The equation 2 – x2 + x3 can be written as 2 + (–1) x2 + x3
We know that, coefficient is the number (along with its sign,i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is -1
, the coefficients of x2 in 2 – x2 + x3 is -1.
(iii) Π/2 x2 +x
Solution:
The equation Π/2x2 +x can be written as (Π/2 ) x2 + x
We know that, coefficient is the number (along with its sign,i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is
, the coefficients of x2 in Π/2x2 +x is Π/2.
(iv)√2x-1
Solution:
The equationx√2x-1 can be written as 0x2 +√2x-1 [Since 0x2 is 0]
We know that, coefficient is the number (along with its sign,i.e., – or +) which multiplies the variable.
Here, the number that multiplies the variable x2 is 0
, the coefficients of x2 in√2x-1 is 0.
Q3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
Binomial of degree 35: A polynomial having two terms and the highest degree 35 is called a binomial of degree 35
Eg., 3x35+5
Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100
Eg., 4x100
Q4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, 5x3 + 4x2 + 7x= 5x3 + 4x2 + 7x1
The powers of the variable x are: 3, 2, 1
, the degree of 5x3 + 4x2 + 7x is 3 as 3 is the highest power of x in the equation.
(ii) 4 – y2
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, in 4 – y2,
The power of the variable y is: 2
, the degree of 4 – y2 is 2 as 2 is the highest power of y in the equation.
(iii) 5t – √7
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, in 5t – √7,
The power of the variable y is: 1
, the degree of 5t – √7 is 1 as 1 is the highest power of y in the equation.
(iv) 3
Solution:
The highest power of the variable in a polynomial is the degree of the polynomial.
Here, 3== 3x0
The power of the variable here is: 0
, the degree of 3 is 0.
Q5. Classify the following as linear, quadratic and cubic polynomials:
Solution:
We know that,
Linear polynomial: A polynomial of degree one is called a linear polynomial.
Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.
Cubic polynomial: A polynomial of degree three a cubic polynomial.
(i) x2 + x
Solution:
The highest power of x2 + x is 2
, the degree is 2
Hence, x2 + x is a quadratic polynomial
(ii) x – x3
Solution:
The highest power of x – x3 is 3
, the degree is 3
Hence, x – x3 is a cubic polynomial
(iii) y + y2 + 4
Solution:
The highest power of y + y2 + 4 is 2
, the degree is 2
Hence, y + y2 + 4 is a quadratic polynomial
(iv) 1 + x
Solution:
The highest power of 1 + x is 1
, the degree is 1
Hence, 1 + x is a linear polynomial
(v) 3t
Solution:
The highest power of 3t is 1
, the degree is 1
Hence, 3t is a linear polynomial
(vi) r2
Solution:
The highest power of r2 is 2
, the degree is 2
Hence, r2 is a quadratic polynomial
Explanation:
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Answer:
1 Find the value of the polynomial 5x – 4x2 + 3 at x = 2 and x = –1
2. Give an example of a monomial and a binomial having degrees as 82 and 99 respectively.
3. Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12.
4. Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12.
Explanation:
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