if alpha and bita are the zeroes of polynomial x^2 +6x+9 ,then form a polynomial whose zeroes are - alpha and - bita
Answers
Step-by-step explanation:
:- x² + 6x + 9
x² + 3x + 3x + 9
x ( x + 3 ) + 3 ( x + 3 )
( x + 3 ) ( x + 3 )
• ( x + 3 ) = 0
x = ( - 3 )
• ( x + 3 ) = 0
x = ( - 3 )
• The new equation having Zeros as :-
So, the Zeros are 3
• Sum of the Zeros are :-
3 + 3 = 6
• Product of the Zeros are :-
3 × 3 = 9
♯ To form the quadratic equation we have formula as :-
x² - ( sum of Zeros )x + ( product of Zeros)
Putting value in it !!
x² - 6x + 9 is the required quadratic equation !!
Answer:
x²-6x-9
Step-by-step explanation:
we are given that alpha(a) and beta(b) are the zeroes of p(x)= x²+6x+9
therefore,
a+b = -6/1
ab= 9/1
now the zeroes of the other polynomial are -a and -b
-a+(-b)=-( a+b)= -(-6)/1= 6/1
and,
-a×(-b)= -(ab) = -9/1
on comparison
the required polynomial is
x²-6x-9
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