Question

If α and β are zeroes of the polynomial 4x²+3x+7 , find the value of 1/α and 1/β

Answer 1

Given Equation is 4x^2 + 3x + 7.

On comparing with ax^2 + bx + c, we get a = 4, b = 3, c = 7.

Now,

Sum of roots = -b/a

= > α + β = -3/4

Product of roots = c/a

= > αβ = 7/4.

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Given :

= > 1/α + 1/β

= > (α+β)/αβ

= > (-3/4)/(7/4)

= > -3/7.

Therefore, the value of 1/α + 1/β = (-3/7).

Hope this helps!