Question

If α, β and γ are the zeros of the polynomial f(x) = ax3+bx2+cx+d then find the value of 1/α+1/β+1/γ.​

Answer 1

Solution : On solving 1/α + 1/β + 1/γ we get,

• (αβ + βγ + αγ)/αβγ

Since we know that,

αβ + βγ + αγ = c/a

αβγ = - d/a

Therefore,

(αβ + βγ + αγ)/αβγ = c/a × a/(- d)

= - c/d

Answer : - c/d

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Explaination :-

• αβ + βγ + γα = Coefficient of x/Coefficient of x³

• αβγ = - Constant Term/Coefficient of x³