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... View Article
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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... 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... 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)... 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)... 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... 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... 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... 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... 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 +... View Article
Which of the following expressions are polynomials? Justify your answer:
(i) 8 (ii) √3x 2 – 2x (iii) 1– √5x (iv)\(\begin{array}{l}\frac{1}{-5x^{2}}+5x+7\end{array} \) (v) (x−2)(x−4)/ x (vi) 1/ x+1 (vii) 1/... 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... 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... 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... 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... 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... 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 =... 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... 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... 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... View Article
