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ol and on the 3e8 229 - 323- 3 you note that has its zexes are de 2 MINT : As a Ba 200 g ple) men (824) is a polynomial

11th - 12th Class
Maths
Solution
86
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( 2 x^{4}-3 x^{3}-3 x^{2}+6 x-2=0 ) If two zero are ( frac{1}{2} & 1 ) Then ( (x-1)left(x-frac{1}{2}right)left(a x^{2}+b x+cright)=2 x^{4}-3 x^{3}-3 x^{2}+6 x-2 ) ( left[x^{2}-frac{3}{2} x+frac{1}{2}right]left[a^{x^{2}}+b x+cright]=2 x^{4}-3 x^{3}-3 x^{2}+6 x-2 ) ( 9 x^{4}+left(5-frac{3 a}{9}right) x^{3}+left(3+frac{a}{2}-frac{3}{8}right) ) ( =3 x^{3}-3 x ) ( a x^{4}+left(-frac{3 a}{2}+bright) x^{3}+left(c+frac{a}{2}-frac{3 b}{2}right) x^{2}+left(-frac{3 c}{2}+frac{b}{2}right) x+frac{1}{2} ) ( =2 x^{4}-3 n^{3}-3 x^{2}+6 x-2+frac{20}{2} ) By Combaring ( frac{c}{8}=-2 Rightarrow(c=-4) ) ( -frac{3 c}{g}+frac{b}{2}=6 Rightarrow frac{c}{c}+frac{b}{g}=6 Rightarrow b=0 ) ( -frac{39}{8}+b=-3 Rightarrow-frac{39}{8}=-3 Rightarrow(29) ) Then ( 2 x^{2}-4=0 ) ( x^{2}=2 Rightarrow(x=pm sqrt{2}) )
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