Question

True and false and give reasons
1) The degree of non-zero constant polynomial is zero.
2) The degree of the zero polynomial is well defined.
3) A binomial may have degree 6.
4) A polynomial cannot have more than one zero
5) The degree of the sum of two polynomials each of degree 6 is always 6.
6) 0 and 2 are the zeroes of y2- 2y.
7) P(x) =x-1 and g(x) =x2-2x +1 . p(x) is a factor of g(x)
8) The factor of 3x2 –x-4 are (x+1)(3x-4)
9) Every linear polynomial has only one zero
10) Every real number is the zero’s of zero polynomial
True and false and give reasons
1) The degree of non-zero constant polynomial is zero.
2) The degree of the zero polynomial is well defined.
3) A binomial may have degree 6.
4) A polynomial cannot have more than one zero
5) The degree of the sum of two polynomials each of degree 6 is always 6.
6) 0 and 2 are the zeroes of y2- 2y.
7) P(x) =x-1 and g(x) =x2-2x +1 . p(x) is a factor of g(x)
8) The factor of 3x2 –x-4 are (x+1)(3x-4)
9) Every linear polynomial has only one zero
10) Every real number is the zero’s of zero polynomial

Answer 1

1 . TRUE

Since degree of constant is zero

2. FALSE

usually it is taken as infinite

3. TRUE

ex: x^6 +y^6

4. FALSE

polynomial can have more than 1 zero

5. TRUE

6. TRUE

y²-2y=0

y(y-2) =0

y=0 or 2

7. TRUE

g(x) = x²-2x+1 = (x-1)²

8. TRUE

9. TRUE

ex: 3x-7 is a linear polynomial

x=7/3 is the zero

10 TRUE

Answer 2

True or False

Find the statements as  true or false :

1)The degree of non-zero constant polynomial is zero.-True

2)The degree of the zero polynomial is well defined.-False

Explanation:The degree of the zero polynomial is infinite.

3)A binomial may have degree 6.-True

Example:$x^{6} -y^{6}$

4)A polynomial cannot have more than one zero-False

Explanation:A polynomial can have more than one zeros.

5)The degree of the sum of two polynomials each of degree 6 is always 6.-True

6)0 and 2 are the zeroes of $y^{2} -2y$.-True

Explanation:$y^{2} -2y=0$

                    $y(y-2)=0$

                    $y=0 (or)y=2$

7)P(x) =x-1 and g(x) =$x^{2} -2x+1$ . p(x) is a factor of g(x)-True

Explanation:$g(x)=x^{2} -2x+1$

                           $=(x-1)^{2}$

8)The factor of $3x^{2} -x-4$ are (x+1)(3x-4)-True

9)Every linear polynomial has only one zero-True

Explanation:$2x-5=0$

                    $x=\frac{5}{2}$which is the zero

10)Every real number is the zero’s of zero polynomial-True