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i)\(p(x) = x + 5\)

ii)\(p(x) = x - 5\)

iii)\(p(x) = 2x + 5\)

iv)\(p(x) = 3x - 2\)

v)\(p(x) = 3x\)

vi)\(p(x) = ax, a \ne 0\)

vii)\(p(x) = cx + d ,c \ne 0\), c,d, are real numbers.

Answer :

i) We have, \(p(x) = x + 5\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow x + 5 = 0 \)

\(\Rightarrow x = -5 \)

Hence, -5 is the zero of given ploynomial.

ii)We have, \(p(x) = x - 5\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow x - 5 = 0\)

\(\Rightarrow x = 5 \)

Hence, 5 is the zero of given ploynomial.

iii)We have, \(p(x) = 2x + 5\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore, p(x) = 0 \)

\(\Rightarrow 2x + 5 = 0\)

\(\Rightarrow x = \frac{-5}{2} \)

Hence,\(\frac{-5}{2} \) is the zero of given ploynomial.

iv) We have, \(p(x) = 3x - 2\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow 3x - 2 = 0\)

\(\Rightarrow x = \frac{2}{3} \)

Hence, \(\frac{2}{3} \) is the zero of given ploynomial.

v) We have, \(p(x) = 3x\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow 3x = 0\)

\(\Rightarrow x = 0 \)

Hence, 0 is the zero of given ploynomial.

vi) We have, \(p(x) = ax\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow ax = 0\)

\(\Rightarrow x = 0, a \ne 0\)

Hence, 0 is the zero of given ploynomial.

vii) We have, \(p(x) = cx + d\)

We also know that, if p(x) = 0 then x is the Zero of the polynomial.

\(\therefore p(x) = 0 \)

\(\Rightarrow cx + d = 0\)

\(\Rightarrow x = \frac{-d}{c} , c \ne 0\)

Hence, \(\frac{-d}{c} \) is the zero of given ploynomial.

- Find the value of the polynomial \(5x - 4x^2 + 3\) at : i) x = 0 ii) x = -1iii) x = 2
- Find p(0), p(1)and p(2) for each of the following polynomials :i)\(p(y) = y^2 -y + 1\)ii)\(p(t) = 2 + t + 2t^2 - t^3\)iii)\(p(x) = x^3\)iv)\(p(x) = (x - 1)(x + 1)\)
- Verify whether the following are zeroes of the polynomial, indicated against them. i)\(p(x) = 3x + 1, x = \frac{-1}{3} \) ii)\(p(x) = 5x - \pi , x = \frac{4}{5} \) iii)\(p(x) = x^2 - 1\), x = 1, -1iv)\(p(x) = (x + 1)(x - 2)\), x = -1, 2v)\(p(x) = x^2\), x = 0vi)\(p(x) = lx + m, x = \frac{-m}{l} \)vii)\(p(x) = 3x^2 - 1\), \(x = \frac{-1}{\sqrt{3}} \), \(\frac{2}{\sqrt{3}} \)viii)\(p(x) = 2x + 1, x = \frac{1}{2} \)

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