# Polynomials

## Exercise 2.2 Part 3

Question 3: Verify whether the following are zeros of the polynomial, indicated against them.

(i) p(x)=3x+1, x=-1/3

Solution: Given, p(x)=3x+1

When x=-1/3

Then p(-1/3)=3xx(-1/3)+1

Or, p(-1/3)=-1+1

Or, p(-1/3)=0

(ii) p(x)=5x-π, x=4/5

Solution: Given p(x)=5x-π

When x=4/5

Then p(4/5)=5xx4/5\-π

Or, p(4/5)=4-π

Or, p(4/5)≠0

(iii) p(x) = x^2 - 1, x =1, - 1

Answer: Given, p(x) = x^2 - 1

At p(1), i.e. x =1

p(1) = 1^2 -1

Or, p(1) = 1 – 1 = 0

At p( - 1), i.e. x = - 1

p( -1) = ( -1)^2 -1

Or, p( -1) = 1 – 1 = 0

Therefore, both 1 and -1 are zeroes of the given polynomial.

(iv) p(x) = (x + 1)(x – 2), x = -1, 2

Answer: When x = - 1

Then, p(1) = ( - 1 + 1)( - 1 – 2)

Or, p(1) = 0 x ( - 3) = 0

When x = 2

Then p(2) = (2 + 1)(2 – 2)

Or, p(2) = 3 xx 0 = 0

Theefore, both – 1 and 2 are zeroes of the given polynomial.

(v) p(x) = x^2, x = 0

Answer: Given, p(x) = x^2

When x = 0

Then p(0) = 0^2

Or, p(0) = 0

Therefore, 0 is the zero of the given polynomial.

(vi) p(x)=lx+m where x=-m/l

Solution: When x=-m/l

Then p(-m/l)=-(m)/(l)xxl+m

Or, p(-m/l)=-m+m

Or, p(-m/l)=0

(vii) p(x)=3x^3-1 where x=-1/sqrt3\,2/sqrt3

Solution: When x=-1/sqrt3

Then p(-1/sqrt3)=3(-1/sqrt3)^2-1

Or, p(-1/sqrt3)=3xx1/3\-1

Or, p(-1/sqrt3)=1-1=0

When x=2/sqrt3

Then p(2/sqrt3)=3(2/sqrt3)^2-1

Or, p(2/sqrt3)=3xx4/3\-1

Pr, p(2/sqrt3)=4-1=3

Thus -1/sqrt3 is the zero of polynomial.

(viii) p(x)=2x+1 where x=1/2

Solution: When x=1/2

Then p(1/2)=2xx1/2\+1

Or, p(1/2)=1+1=2

Thus, ½ is not the zero of the polynomial.