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Class ten Chap 2 Polynomial NCERT Solutions maths

Chapter 2: Polynomials NCERT Solutions

TEXTBOOK’S EXERCISE – 2.2

2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
 

Sol. We know that a quadratic polynomial with zeroes α and β is given by

∴ A required quadratic polynomial is

∴ A required quadratic polynomial is

∴ A required quadratic polynomial is x2+ √5.

∴ A required quadratic polynomial is x2 – x + 1.

∴ A required quadratic polynomial is

∴ A required quadratic polynomial is x2 – 4x + 1

TEXTBOOK’S EXERCISE – 2.3

1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the fol­lowing :

  • P(x) = x3– 3x2 + 5x -3

g(x) = x2-2 

  • P(x) =x4– 3x2 + 4x -3

g(x) = x2+1-x

  • P(x) = x4– 5x +6

g(x) = 2 – x2

∴ By division algorithm,

x3– 3x2 + 5x -3= (x-3)(x2-2)+(7x-9)

Here, quotient = x – 3 and remainder = 7x – 9

By division algorithm,

By division algorithm,

x4 – 5x2 + 6 = (–x2 – 2)(–x2 + 2) + (–5x + 10)

Here, quotient = − x2 −2

and remainder = – 5x + 10

2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :

Since, remainder is zero, therefore

 t2 – 3 is factor of 2t4 + 3t3 – 2t2 – 9t – 12.

Since, remainder is 0, therefore, x2 + 3x + 1 is a factor of 3x4 + 5x3 – 7x2 + 2x + 2

Since, remainder is not zero, therefore, x3 – 3x + 1 is not a factor of x5 – 4x3 + x2 + 3x + 1.

3. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are

Sol. Since two zeroes are

factors of the given polynomial.

is a factor of the given polynomial. Now, let us divide the given polynomial by

No, factorizing

Hence, g (x) = x2 – x + 1

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