Q30 of 40 Page 1

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x)=a x2+bx + c, a ≠ 0, c ≠ 0

OR


Divide the polynomial f(x)=3 x2-x3-3 x+5 by the polynomial g(x)=x-1-x2 and verify the division algorithm.


ax2 + bx + c, let its zeroes be α and β we have to find a quadratic polynomial whose zeroes are

Now , to form equation we need to find


∴ Required quadratic equation will be



Now,




According to division algorithm


F(x) = g(x). q(x) + r (x)


q(x) = - x2 + x -1


q(x) = x-2


r(x) = 3


RHS = (-x2+x-1)(x-2)+3


= -x3+2x2+x2-2x-x+2+3


= -x3 +3x2-3x+5


= LHS


Hence verified


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OR


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OR


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