Question

If alpha and beta are two zeros of the polynomial f(x)= ax2+bx+c find the value of 1/alpha + 1/beta

Answer 1

If alpha and beta are the zeroes of the polynomial p(x)=ax²+bx+c

We know that,

alpha+beta = -b/a

alpha×beta = c/a

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } \\ = \frac{ \frac{ - b}{a} }{ \frac{c}{a} } = \frac{ - b}{c}$

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Answer 2

Answer

-b/c

Solution

Given:

polynomial f(x) = ax² + bx + c

If α and β are the zeroes of f(x)

then

sum of the zeroes = -coefficient of x / coefficient of x²

=> α + β = -b/a

Product of the zeroes = constant term / coefficient of x²

=> αβ = c/a

Now:

1/ α + 1/ β

=> (β + α) / αβ {Taking LCM}

=> (α + β) / αβ {∵ α + β = β + α}

=> -b/a ÷ c/a

=> -b/a × a/c

=> -b/c