SOLUTION: if one root of the equation (p^2+2)x^2+7x+3p=0 is the reciprocal of the another then find the value of p

Question 955784: if one root of the equation (p^2+2)x^2+7x+3p=0 is the reciprocal of the another then find the value of p

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Let be one root. Then the other root will be . Consequently, their product will be . This is true if is nonzero.
Now, let . => ,,
If , then we are given that the roots are and .

since product of roots is , we have
=>

=> or
=>

since SUM OF THE ROOTS is

Computing for :
if

or
where -roots are reciprocal to each other
Thus, the actual roots are:
or

second solution:
if

...solving this using quadratic formula you will get

or
where =>
check our function: if

roots are: or which are reciprocal to each other

and, if

roots are: => or and they are reciprocal to each other

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