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Find the zeroes of the polynomial: p( ) = ( -2)²−( + 2)²

Solution p(x) = ( –2)2−( + 2)2 Zero of the polynomial p(x) = 0 Hence, ⇒ (x–2)2−(x +... View Article

Find the zeroes of the polynomial in each of the following: (i) p(x) = x – 4 (ii) g(x) = 3 – 6x (iii) q(x) = 2x -7 (iv) h(y) = 2y

Solution (i) p(x) = x – 4 Zero of the polynomial p(x) ⇒ p(x) = 0 P(x) = 0 ⇒ x – 4= 0 ⇒ x = 4 Thus, the... View Article

Verify whether the following are true or false: (i) -3 is a zero of x – 3 (ii) – 1/3 is a zero of 3x + 1 (iii) – 4/5 is a zero of 4 -5y (iv) 0 and 2 are the zeroes of t² – 2t (v) -3 is a zero of y² + y – 6

Solution (i) –3 is a zero of x – 3 The given statement is False Zero of x – 3 can be determined as x – 3 = 0... View Article

Find p(0), p(1), (−2) for the following polynomials: (i) ( ) = 10 −4 ² -3 (ii) ( ) = (y + 2) (y – 2)

Solution (i) ( )=10 −4 2 –3 p(x) = 10 −4 2 –3 When x = 0, p(x) = p(0) On substituting x = 0, p(0) =... View Article

If p( ) = ² – 4 + 3, evaluate: (2)− (−1) + (1/2).

Given p( ) = 2 – 4 + 3 According to the given details When x = 2, p(x) = p(2) p( ) = 2 – 4 + 3... View Article

Find the value of the polynomial 3 ³ – 4 ² + 7 – 5, when x = 3 and also when x = -3.

Given p(x) = 3 3 – 4 2 + 7 – 5 According to the given details When x = 3, p(x) = p(3) p(x) = 3... View Article

Give an example of a polynomial, which is: (i) monomial of degree 1 (ii) binomial of degree 20 (iii) trinomial of degree 2

Solution (i) monomial of degree 1 A monomial is an algebraic expression that has only one term. An example of a polynomial, which is a... View Article

Classify the following as a constant, linear, quadratic and cubic polynomials: (i) 2 – x² + x³ (ii) 3x³ (iii) 5t – √7 (iv) 4 – 5y² (v) 3 (vi) 2 + x (vii) y³ – y (viii) 1 + x + x² (ix) t² (x) √2x – 1

Solution A degree of a polynomial is the highest or the greatest power of a variable in a polynomial equation. The degree indicates The... View Article

Write the coefficient of x²in each of the following: (i) (π/6)x + x² – 1 (ii) 3x – 5 (iii) (x -1) (3x – 4) (iv) (2x – 5) (2x² – 3x + 1)

Solution A coefficient is an integer that is multiplied to the variable of a single term or the terms of a given polynomial. ... View Article

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

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