- What must be added to polynomial f(x)=x4+2x3-2x2+x-1 so that the resulting polynomial is excatly divisible by x2+2x-3?
- Find the zero's of the polynamial 4x2-7.
- Find all the zero's of the polynomial 2x3+x2-6x-3, if 2 of its zero's are minus root 3 and root 3.
- Find the zero's of the quadratic polynomial x2=5x=6 and verify the relationship between the zero's and the co-efficient.
- if alpha, beta are zero's of the polynomial x2-2x-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 x2 + 2x – 3.
(2)
4x2 - 7 = 0
4x2 = 7
x2 = 7/2
x = ± (sqrt7)/2
Thus, zeroes of the given polynomials are (sqrt7)/2 and -(sqrt7)/2
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