Question

if the zeroes of the polynomial x3 - 5x2 + 2x +3 are x, x+y and x-y, find x

Answer 1

Step-by-step explanation:

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>>Relationship between Zeroes and Coefficients of a Polynomial

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Question

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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)=2x+5

(iv) p(x)=3x−2

(v) p(x)=3x

(vi) p(x)=ax,a



=0

(vii) p(x)=cx+d,c



=0,c,d are real numbers.

Medium

Solution

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To find zero of the polynomial, p(x)=0

(i) If p(x)=x+5=0 then x=−5, i.e. −5 is the zero.

(ii) If p(x)=x−5=0 then x=5, i.e. 5 is the zero.

(iii) If p(x)=2x+5=0 then x=

2

−5

, i.e.

2

−5

is the zero.

(iv) If p(x)=3x−2=0 then x=

3

2

, i.e.

3

2

is the zero.

(v) If p(x)=3x=0 then x=0, i.e. 0 is the zero.

(vi) If p(x)=ax=0 then x=0, i.e. 0 is the zero.

(vii) If p(x)=cx+d=0 then x=

c

−d

, i.e.

c

−d

is the zero.