Question:
if alpha and beta are zeros of polynomial x2 6x 9,then form a polynomial whose zeros are -alpha and -beta.
Answer:
Given, equation is: x2 + 6x + 9
Again, α and β are the zeroes of the equation.
Now, α + β = -6
and α * β = 9
Now, equation of polynomial whose zeroes are -α and -β is
x2 - {(-α) + (-β)}x + (-α) * (-β)
= x2 - (-α - β)x + α * β
= x2 + (α + β)x + α * β
= x2 + (-6)x + 9
= x2 - 6x + 9
So, the equation of polynomial is: x2 - 6x + 9
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