If alpha and beta are the roots of 4x^2 + 3x + 7 = 0 , then find the value of 1/ alpha + 1/ beta .
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Answer:
3/7
Step-by-step explanation:
For quadratic equations in form of ax^2 + bx + c = 0,
Sum of roots = -b/a
Product of roots = c/a
In the given equation 4x^2 - 3x + 7 = 0
a = 4 ; b = -3 ; c = 7
∴ if α and β are the roots ,
⇒ α + β = - (-3/4) = 3/4
As well as, αβ = 7/4
∴ 1/α + 1/β = (β + α)/αβ
= ( 3/4 ) / (7/4)
= 3/7
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