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Question
If α and β are the zeros of the quadratic polynomial f(x)=x2−3x−2, find a quadratic polynomial whose zeros are 12α+β and 12β+α
If α and β are the zeros of the quadratic polynomial f(x)=x2−3x−2, find a quadratic polynomial whose zeros are 12α+β and 12β+α
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Solution
If 
and 
are the roots of 
then 
+
=3 and 
= -2
So the equation with roots as 
Sum of roots = 
+
=
Product of roots = (
)(
) = 
Equation =
and are the roots of then
+=3 and = -2So the equation with roots as
Sum of roots =
+=Product of roots = (
)() = Equation =
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