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Question

If alpha and ß are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -alpha, -ß.


Solution

If alpha and ß are zeroes of polynomial x²+6x+9

then alpha * ß(product of zeroes) =c/a =9/1 =9=>alpha * ß=9 ---(1)

 alpha * ß(sum of zeroes) =-b/a =-6/1 =-6 =>alpha + ß= -6  ----(2)

Now zeroes of new quadratic equation are  -alpha, -ß.

sum of zeroes = -alpha+ -ß =  -(alpha + ß)

                      from (2) = --6 =6  ---(3)

product of zeroes = -alpha * -ß =  -alpha * -ß =alpha * ß

                      from (1) = 9   ----(4)

Quadratic equation if of the form  x² -(sum of zeroes)x +product of zeroes

=x² -(6)x + 9

=x² -6x + 9

 

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