if one zero of p(x)=(a²+4)x²+13x+4a is reciprocal at other , then find the value of a
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Answered by
38
product of root =constant term/coefficient of x^2
so, 1=4a/(a^2+4)
a^2+4=4a
a^2-4a+4=0
(a-2)^2=0
a=2
so, 1=4a/(a^2+4)
a^2+4=4a
a^2-4a+4=0
(a-2)^2=0
a=2
Answered by
8
LET @ BE ONE OF THE ZERO OF GIVEN POLYNIMIAL .
THEN ANOTHER ZERO IS 1/@.
NOW,WE KNOW THAT
PRODUCT OF ZEROES=CONSTANT\COEFFUCIENT OF X^SQUARE
@×1\@ =4a/a^squ.+4
1 =4a/a^squ. +4a
on solving the equation you will get a=2.ans
THEN ANOTHER ZERO IS 1/@.
NOW,WE KNOW THAT
PRODUCT OF ZEROES=CONSTANT\COEFFUCIENT OF X^SQUARE
@×1\@ =4a/a^squ.+4
1 =4a/a^squ. +4a
on solving the equation you will get a=2.ans
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