3.Verify whether the following are zeroes of the polynomial, indicated against them.
i)$$p(x) = 3x + 1$$, x = -1/3
ii)$$p(x) = 5x - \pi$$, x = 4/5
iii)$$p(x) = x^2 - 1$$, x = 1, -1
iv)$$p(x) = (x + 1)(x - 2)$$, x = -1, 2
v)$$p(x) = x^2$$, x = 0
vi)$$p(x) = lx + m$$, x = -m/l
vii)$$p(x) = 3x^2 - 1$$, $$x = -1/\sqrt{3}$$, $$2/\sqrt{3}$$
viii)$$p(x) = 2x + 1$$, x = 1/2

i)$$p(x) = 3x + 1$$
To check, if x = -1/3 is zero of given polynomial then p(-1/3) should be equal to 0.
So, p(-1/3) = 3(-1/3) + 1 = -1 +1 = 0
Therefore, x = -1/3 is zero of given polynomial.

ii)$$p(x) = 5x - \pi$$
To check, if 4/5 is zero of given polynomial then p(4/5) should be equal to 0.
So, $$p(4/5) = 5(4/5) - \pi = 4 - \pi$$
Therefore, x = 4/5 is not a zero of given polynomial.

iii)$$p(x) = x^2 - 1$$
To check, if x = 1 is zero of given polynomial then p(1) should be equal to 0.
So, p(1) = $$1^2 - 1$$ = 1 - 1 = 0
Therefore, x = 1 is a zero of given polynomial.
To check, if x = -1 is zero of given polynomial then p(-1) should be equal to 0.
So, p(-1) = $${-1}^2 - 1$$ = 1 - 1 = 0
Therefore, x = 1 is too, a zero of given polynomial.

iv)$$p(x) = (x + 1)(x - 2)$$
To check, if x = -1 is zero of given polynomial then p(-1) should be equal to 0.
So, p(-1) = (-1 + 1)(-1 - 2) = 0 × -3 = 0
Therefore, x = -1 is zero of given polynomial.
To check, if x = 2 is zero of given polynomial then p(2) should be equal to 0.
So, p(2) = (2 + 1)(2 - 2) = 3 × 0 = 0
Therefore, x = 2 is too, a zero of given polynomial.

v)$$p(x) = x^2$$
To check, if x = 0 is zero of given polynomial then p(0) should be equal to 0.
So,$$p(0) = (0^3) = 0$$
Therefore, x = 0 is zero of given polynomial.

vi)$$p(x) = lx + m$$
To check, if x = -m/l is zero of given polynomial then p(-m/l) should be equal to 0.
So, p(-m/l) = l(-m/l) + m = -m + m = 0
Therefore, x = -m/l is zero of given polynomial.

vii)$$p(x) = 3x^2 - 1$$
To check, if$$x = -1/\sqrt{3}$$ is zero of given polynomial then p($$-1/\sqrt{3}$$) should be equal to 0.
So, p($$-1/\sqrt{3}$$) = $$3(-1/\sqrt{3})^2 - 1$$ = 1 - 1 = 0
Therefore,$$x = -1/\sqrt{3}$$ is zero of given polynomial.
To check, if $$x = 2/\sqrt{3}$$ is zero of given polynomial then p($$2/\sqrt{3}$$) should be equal to 0.
So, p($$2/\sqrt{3}$$) = $$3(2/\sqrt{3})^2 - 1$$ = 3
Therefore, $$x = 2/\sqrt{3}$$ is not a zero of given polynomial.

viii)$$p(x) = 2x + 1$$
To check, if x = 1/2 is zero of given polynomial then p(1/2) should be equal to 0.
So, p(1/2) = 2(1/2) + 1 = 1 + 1 = 2
Therefore, x = 1/2 is not a zero of given polynomial.