If ∝and β are the zeroes of the quadratric polynomial f(x) =x2 -3x -2,
find a quadratic polynomial whose zeroes are 1/(2α+ β) and 1/(2β+ α) .
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Step-by-step explanation:
Aloha !
Given,.
p(x)=x²-3x-2
Let,
x²-3x-2=0
x²-2x-x-2=0
-x(-x-2)+1(-x-2)=0
(-x-2)(-x+1)=0
-x-2=0 (or) -x+1=0
-x=2. (or) -x= -1
x= -2 (or) x=1
Sum of roots= -2+1= -1
product of roots= -2×1= -2
Quadratic equation:-
X²- (sum of roots) X + product of roots=0
X²-(-1)X+(-2)=0
X²+X-2=0
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