Relationship of Zeros With Coefficients of Cubic Polynomial
Relationship of Zeros With Coefficients of Cubic Polynomial
Relationship of zero with coefficients of cubic polynomial:
A cubic polynomial ,
has exactly three zeros. Let these be
then
[sum of the zeros]
[sum of the product of zeros taken two at a time]
[product of zeros]
Example: Verify that 1/2, 1, -2 are zeros of Also verify the relationship between the zeros and the coefficients.
Solution: Let
we have
and
Thus, are zeros of f(x).
We have
Note that in each case LHS = RHS.
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