Polynomials Exercise 2.4

NCERT solutions for Class 10 Maths Polynomials 

NCERT Solutions for Class 10 Maths Polynomials

1. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

(i)

(ii)

Ans. (i) Comparing the given polynomial with , we get

and

= = = 0

= = 0

= = = 0

and are the zeroes of

Now,

=

And

=

= =

And =

(ii) Comparing the given polynomial with , we get

and

= = 0

= = 0

and are the zeroes of

Now,

=

And =

= =

And =

NCERT Solutions for Class 10 Maths Exercise 2.4

2. Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and the product of its zeroes are respectively.

Ans. Let the cubic polynomial be and its zeroes be and

Then = 2 = and =

And =

Here, and

Hence, cubic polynomial will be

NCERT Solutions for Class 10 Maths Exercise 2.4

3. If the zeroes of the polynomial are find and

Ans. Since are the zeroes of the polynomial

=

And

=

Hence and .

NCERT Solutions for Class 10 Maths Exercise 2.4

4. If the two zeroes of the polynomial are find other zeroes.

Ans. Since are two zeroes of the polynomial

Let

Squaring both sides,

Now we divide by to obtain other zeroes.

=

=

=

=

and are the other factors of

and 7 are other zeroes of the given polynomial.

NCERT Solutions for Class 10 Maths Exercise 2.4

5. If the polynomial is divided by another polynomial the remainder comes out to be find and

Ans. Let us divide by .

Remainder =

On comparing this remainder with given remainder, i.e.

And