SOLUTION: Find an equation whose roots are the reciprocals of the roots of the equation 5x^2 + 15x - 2= 0
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Question 563703: Find an equation whose roots are the reciprocals of the roots of the equation 5x^2 + 15x - 2= 0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the quadratic formula:
})
Flip the fractions and rationalize the new denominators (see Rationalizing Denominators if you need a refresher here)
To obtain:
Then
\right)\ =\ 0)
and
\right)\ =\ 0)
Hence
\right)\left(x\ -\ \left(\frac{-15\ -\ \sqrt{265}}{4}\right)\right)\ =\ 0)
First, simplfy the signs:
\right)\left(x\ +\ \left(\frac{15\ +\ \sqrt{265}}{4}\right)\right)\ =\ 0)
Then use FOIL to multiply the two binomials. Note that the second terms are a conjugate pair so their product is the difference of two squares.
Finally, multiply through by the denominator of the first degree and constant coefficients to write the equation with integer coefficients.
John
My calculator said it, I believe it, that settles it
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