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- What must be added to polynomial f
^{(x)}=x^{4}+2x^{3}-2x^{2}+x-1 so that the resulting polynomial is excatly divisible by x^{2}+2x-3? - Find the zero's of the polynamial 4x
^{2}-7. - Find all the zero's of the polynomial 2x
^{3}+x^{2}-6x-3, if 2 of its zero's are minus root 3 and root 3. - Find the zero's of the quadratic polynomial x
^{2}=5x=6 and verify the relationship between the zero's and the co-efficient. - if alpha, beta are zero's of the polynomial x
^{2}-2x-8,then form a quadratic polynomial whose zero's are 2alphaand 2beta.

^{(x)}=x^{4}+2x^{3}-2x^{2}+x-1 so that the resulting polynomial is excatly divisible by x^{2}+2x-3?^{2}-7.^{3}+x^{2}-6x-3, if 2 of its zero's are minus root 3 and root 3.^{2}=5x=6 and verify the relationship between the zero's and the co-efficient.^{2}-2x-8,then form a quadratic polynomial whose zero's are 2alphaand 2beta.**(1)**

Consider, division of .

Remainder = – *x* + 2

so, – (– *x *+ 2) = *x* – 2, should be added to *p*(*x*) to make it exactly divisible by *x*^{2} + 2*x* – 3.

**(2)**

4*x*^{2 }- 7 = 0

4*x*^{2 }= 7

*x*^{2 }= 7/2

*x*^{ }= ± (sqrt7)/2

Thus, zeroes of the given polynomials are (sqrt7)/2 and -(sqrt7)/2

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