Question

if alpha,beta be the roots of the quadratic equation 3x^2+4x-7=0,then find the value of 1/alpha+1/beta

Answer 1

hope this helps you.........

Answer 2

If α, β be the roots of the quadratic equation 3x² + 4x - 7 = 0

To find : Value of

$\frac{1}{ \alpha } + \frac{1}{ \beta }$

For a quadratic equation ax² + bx + c = 0

Sum of roots = - b/a

Product of roots = c/a

Quadratic equation : 3x² + 4x - 7 = 0

Sum of roots = - 4/3

Product of roots = - 7/3

Since α, β are roots,

α + β = - 4/3

αβ = - 7/3

$\implies \frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ \implies \: \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ \implies \: \frac{ \frac{ - 4}{3} }{ \frac{ - 7}{3} } \\ \\ \implies \frac{4}{7}$

Therefore,

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{4}{7}$