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Determine the degree of each of the following polynomials: (i) 2x – 1 (ii) -10 (iii) x² – 9x + 3x⁵ (iv) y² (1 – y²)

The highest or greatest degree of a variable in a polynomial is called the degree of a polynomial.A polynomial’s degree is the highest or... View Article

Classify the following polynomials as polynomials in one variable, two variables etc. (i) x² + x + 1 (ii) y² – 5y (iii) xy + yz + zx (iv) x² – 2xy + y² + 1

(i) x2 + x + 1(ii) y3 – 5y(iii) xy + yz + zx(iv) x2 – 2xy + y2 + 1 Solution (i) x2 + x + 1 The given... View Article

Which of the following expressions are polynomials? Justify your answer:

(i) 8 (ii) √3x 2 – 2x (iii) 1– √5x (iv) (v) (x−2)(x−4)/ x (vi) 1/ x+1 (vii) 1/ 7 a 3 – 2... View Article

One of the zeroes of the polynomial 2x² + 7x -4 is (A) 2 (B) 1/2 (C) – 1/2 (D) -2

The correct answer is (B) 1/2 Solution Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A... View Article

Zero of the polynomial p(x) = 2x + 5 is (A) – 2/5 (B) – 5/2 (C) 2/5 (D) 5/2

The correct answer is (B) – 5/2 Solution Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.... View Article

Zero of the zero polynomial is (A) 0 (B) 1 (C) Any real number (D) Not defined

The correct answer is (C) Any real number Solution A zero polynomial is the one where all the coefficients are equal to zero. So, the degree of... View Article

If p(x) = x + 3, then p(x) + p(-x) is equal to (A) 3 (B) 2x (C) 0 (D) 6

The correct answer is (D) 6 Solution p(x) = x + 3 p(– x) = – x + 3 Hence p(x) + p(–x) = (x + 3) + (– x + 3) = x + 3... View Article

The value of the polynomial 5x – 4x² + 3, when x = – 1 is (A) – 6 (B) 6 (C) 2 (D) – 2

The correct answer is (A) – 6 Solution p(x) = 5x – 4x2 + 3 To obtain p(– 1), let us substitute x = -1, p(– 1) =... View Article

If p(x) = x² – 2√2x + 1, then p(2√2) is equal to (A) 0 (B) 1 (C) 4√2 (D) 8√2 + 1

The correct answer is (B) 1 Solution p(x) = x2 – 2√2x + 1 To obtain p(2√2), let us substitute x = 2√2,... View Article

Degree of the zero polynomial is (A) 0 (B) 1 (C) Any natural number (D) Not defined

The correct answer is (D) Not defined Solution The degree of a polynomial is the highest power of the variable in a polynomial expression.... View Article

Degree of the polynomial 4×⁴ + 0x³ + 0x⁵ + 5x + 7 is (A) 4 (B) 5 (C) 3 (D) 7

The correct answer is (A) 4 Solution The degree of a polynomial is the highest power of the variable in a polynomial expression. The... View Article

Represent geometrically the following numbers on the number line: (i) √4.5 (ii) √5.6 (iii) √8.1 (iv) √2.3

Solution (i) √4.5 Draw a line segment such that AB = 4.5 units. Place the point C at a distance of 1 unit from B. Mark O as the... View Article

Locate √5, √10 and √17 on the number line.

Let us represent √5 on the number line: 5 can be written as the sum of the square of two natural numbers: 5 =1+ 4 =12 + 22 On... View Article

Represent the following numbers on the number line: 7, 7.2, −3/2 , −12/5

To represent 7, 7.2, −3/2 , −12/5... View Article

Insert a rational number and an irrational number between the following: (i) 2 and 3 (ii) 0 and 0.1 (iii) 1/3 and 1/2 (iv) – 2/5 and 1/2 (v) 0.15 and 0.16 (vi) √2 and √3 (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 6.375289 and 6.375738.

Solution (i) 2 and 3 Rational number between 2 and 3 = 2.7 Irrational number between 2 and 3 = 2.312312312..... (ii) 0 and 0.1... View Article

Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) 5/7 and 6/7 (iv) 1/4 and 1/5

Solution (i) –1 and –2 Three rational numbers between –1 and –2 are –1.1, –1.2 and –1.3. (ii) 0.1... View Article

Find which of the variables x, y, z and u represent rational numbers and which irrational numbers: (i) x2 = 5 (ii) y2 = 9 (iii) z2 = .04 (iv) u2 = 17/4

Solution Let us solve the given equations (i) x2 = 5 On simplifying, we obtain ⇒ x = ± √5 Therefore, x is... View Article

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

Solution The answer is No. If we consider x as rational number and y as irrational number Then the product of xy is not... View Article

Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.

Solution We know that the sum of rational and irrational number is mainly an irrational number. If we consider x as rational number... View Article

The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0 , is (A) 19/10 (B) 1999/1000 (C) 2 (D) 1/9

The correct answer is (C) 2 Solution Let us simplify the given choices (A) 19/10 = 1.9 (B) 1999/1000= 1.999 (C) 2 (D) 1/9= 0.111….... View Article