Find the zero of the polynomial in each of the following cases:(i) $p(x)=x+5$(ii) $p(x)=x-5$(iii) $p(x)=2 x+5$(iv) $p(x)=3 x-2$(v) $p(x)=3 x$(vi) $p(x)=a x, a ≠ 0$(vii) $p(x)=c x+d, c ≠ 0, c, d$ are real numbers.

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To do:

We have to find the zeroes of the given polynomials.

Solution :

The zero of a polynomial is defined as any real value of $x$, for which the value of the polynomial becomes zero.

Therefore,

(i) Zero of the polynomial $p(x) = x+5$ is,

$x+5 = 0$

$x = -5$.

Zero of the polynomial $p(x) = x+5$ is $-5$.

(ii) Zero of the polynomial $p(x) = x-5$ is,

$x-5 = 0$

$x = 5$.

Zero of the polynomial $p(x) = x-5$ is $5$.

(iii) Zero of the polynomial $p(x) = 2x+5$ is,

$2x+5 = 0$

$2x = -5$

$x=\frac{-5}{2}$

Zero of the polynomial $p(x) = 2x+5$ is $\frac{-5}{2}$.

(iv) Zero of the polynomial $p(x) = 3x-2$ is,

$3x-2 = 0$

$3x = 2$

$x=\frac{2}{3}$

Zero of the polynomial $p(x) = 3x-2$ is $\frac{2}{3}$.

(v) Zero of the polynomial $p(x) = 3x$ is,

$3x = 0$

$x = 0$.

Zero of the polynomial $p(x) = 3x$ is $0$.

(vi) Zero of the polynomial $p(x) = ax$ is,

$ax = 0$

$x = \frac{0}{a}$

$x=0$

Zero of the polynomial $p(x) = ax$ is $0$.

(vii) Zero of the polynomial $p(x) = cx+d$ is,

$cx+d = 0$

$cx = -d$

$x=\frac{-d}{c}$

Zero of the polynomial $p(x) = cx+d$ is $\frac{-d}{c}$.

Updated on 10-Oct-2022 13:39:07

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