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- Geometric Meaning of the Zero's of the polynomial
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- Relation between coefficient and zero’s of the Polynomial
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- Formation of polynomial when the zeros are given
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- Division algorithm for Polynomial

- Ncert Solutions Exercise 1
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1) Find a quadratic polynomial whose zeroes are 5 + √2 and 5 -√2

2) If a and b are zeroes of quadratic polynomial kx

3) If one zero of 3x

4) If p and q are the zeroes of p(x) = kx

5) If a and b are zeroes of x

6) If one zero of the quadratic polynomial x

7) Find the zeroes of the quadratic polynomial x

8) Find the value of a and b, if they are the zeroes of polynomial x

9) If m and n are the zeroes of the polynomial 3x

10) Show that 2, -1 and 1/2 are the zeroes of the cubic polynomial

p(x) = 2x

and then verify that the sum of the zeroes =-(Coeff of x

11) Find the zeroes of the polynomial f(x) = 4√3 x

12) If p and q are the zeroes of the polynomial f(x) = x

13) If p and q are the zeroes of the quadratic polynomial f(x) = kx

15) If a and b are the zeroes of the quadratic polynomial f(x) = x

16) If two zeroes of the polynomial f(x) = x

17) If l and m are zeroes of the polynomial p(x) = 2x

18) If p ,q and r are zeroes of polynomial 6x

19) If the zeroes of the polynomial f(x) = ax

20) Obtain all zeroes of the polynomial f(x) = 2x

Answer

1) x

2) 2/3,-1

3) p=3

4) k=3/2

6) -16

7) -4 and -4

8) a=1 and b=-2

9) -145/12

11) -2/ √3, √3/4

12) 6

13) -1,2/3

14) 108

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