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CLASS 9 MATHS CHAPTER 2 POLYNOMIALS

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Answered by tennetiraj86
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Step-by-step explanation:

Solutions :-

i) Given Polynomial P(x) = 3x+1

If x=-1/3 is a zero of P(x) then it satisfies the given polynomial.

=>P(-1/3) = 3(-1/3)+1

=>P(-1/3)= (-3/3)+1

=> P(-1/3)=-1+1

P(-1/3)=0

x= -1/3 is the zero of the polynomial p(x)=3x+1

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ii)Given polynomial P(x)=5x-π

If x= 4/5 is a zero of P(x) then it satisfies the given polynomial.

=> P(4/5)=5(4/5)-π

=>P(4/5)=4-π

Since P(4/5)≠0 then x= 4/5 is not the zero of the polynomial .

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iii) Given Polynomial P(x)=x^2-1

If x= 1 is a zero of P(x) then it satisfies the given polynomial.

=>P(1)=(1)^2-1

=>P(1)=1-1

=>P(1)=0

x=1 is the zero of the polynomial of P(x)=x^2-1

If x= -1 is a zero of P(x) then it satisfies the given polynomial.

=>P(-1)=(-1)^2-1

=>P(-1)=1-1

=>P(-1)=0

x=-1 is the zero of the polynomial of P(x)=x^2-1

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iv) Given Polynomial P(x)=(x+1)(x-2)

If x= -1 is a zero of P(x) then it satisfies the given polynomial.

=>P(-1)=(-1+1)(-1-2)

=>P(-1)=(0)(-3)

=>P(-1)=0

x=-1 is the zero of the polynomial of P(x)=(x+1)(x-2)

If x= 2 is a zero of P(x) then it satisfies the given polynomial.

=>P(2)=(2+1)(2-2)

=>P(2)=(3)(0)

=>P(2)=0

x=2 is the zero of the polynomial of P(x)=(x+1)(x-2)

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v)Given Polynomial P(x)=x^2

If x= 0 is a zero of P(x) then it satisfies the given polynomial.

=>P(0)=(0)^2

=>P(0)=0

=>P(0)=0

x=0 is the zero of the polynomial of P(x)=x^2

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vi)Given Polynomial P(x)=lx+m

If x= -m/l is a zero of P(x) then it satisfies the given polynomial.

=>P(-m/l)=l(-m/l)+m

=>P(-m/l)=(-lm/l)+m

=>P(-m/l)=(-m)+m

=>P(-m/l)=0

x=-m/l is the zero of the polynomial of P(x)=lx+m

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vii)Given Polynomial P(x) = 3x^2-1

If x=-1/√3 is a zero of P(x) then it satisfies the given polynomial.

=>P(-1/√3) = 3(-1/√3)^2-1

=> P(-1/√3)=3(1/3)-1

=> P(-1/√3)=(3/3)-1

=> P(-1/√3)=1-1

=>P(-1/√3)=0

x= -1/√3 is the zero of the polynomial p(x)=3x^2-1

If x=-2/√3 is a zero of P(x) then it satisfies the given polynomial.

=>P(2/√3) = 3(2/√3)^2-1

=> P(2/√3)=3(4/3)-1

=> P(2/√3)=(12/3)-1

=> P(2/√3)=4-1

=>P(2/√3)=3

x= 2/√3 is not the zero of the polynomial p(x)=3x^2-1

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viii)Given Polynomial P(x) = 2x-1

If x=1/2is a zero of P(x) then it satisfies the given polynomial.

=>P(1/2) = 2(1/2)-1

=> P(1/2)=(2/2)-1

=> P(1/2)=1-1

P(1/2)=0

x= 1/2 is the zero of the polynomial p(x)=2x-1

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Answers:-

i)x= -1/3 is the zero of the polynomial p(x)=3x+1

ii)x= 4/5 is not the zero of the polynomial .

iii)x=1 is the zero of the polynomial of P(x)=x^2-1

x=-1 is the zero of the polynomial of P(x)=x^2-1

iv)x=-1 is the zero of the polynomial of P(x)=(x+1)(x-2)

x=2 is the zero of the polynomial of P(x)=(x+1)(x-2)

v)x=0 is the zero of the polynomial of P(x)=x^2

vi)x=-m/l is the zero of the polynomial of P(x)=lx+m

vii)x= -1/√3 is the zero of the polynomial p(x)=3x^2-1

x= 2/√3 is not the zero of the polynomial p(x)=3x^2-1

viii)x= 1/2 is the zero of the polynomial p(x)=2x-1

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Used formulae:-

If a is a zero of the polynomial P(x) then it satisfies the P(x). i.e. P(a) = 0

It is also known as factor theorem .

Factor Theorem:-

P(x) be a polynomial of the degree greater than or equal to 1 and x-a is a factor of P (x) is P(a)=0 vice-versa.

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