If α,  β  are the roots of the equation 2x2−3x−5=0,  then the equation whose roots are 5/α,  5/β is:

2x2−3x−5=0, ∴ α+β=3/2,  αβ=−5/2 σ1=5/α+5/β=5(α+β)/αβ=−3    and σ2=25/αβ=−10 ∴  Required equation is x2+3x−10=0