Question

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

Answer 1

for ax² + bx + c = 0

α + β = -b / a
αβ = c/a

1/α + 1/β = (α + β) / αβ = - b / c

here, b = 3 and c = -7

So answer is  - 3/7

Answer 2

Hey dear !!!

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==> In the given equation ,

p(x) = 4x² + 3x + 7

And α = alpha , β = beta are the zeroes of the given polynomial .

We have to find the value of ,

$\frac{1}{ \alpha } + \frac{1}{ \beta }$
So, lets find this,

We have the following values ,as

a = 4

b = 3

c = 7

We know that,

$\alpha + \: \beta = \frac{ - b}{a} \\ \\ = \frac{ - 3}{4}$
Also we know that,

$\alpha \beta = \frac{c}{a} \\ \\ = \frac{7}{4}$

Now, by using the identity of quadratic expression ,
$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta }$
By putting the obtained value we get,



$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ = \frac{ - 3 \div 4}{7 \div 4} \\ \\ 4 \: and \: 4 \: get \: cancelled \: now \: we \: get \\ \\ = \frac{ - 3}{7}$
Therefore 1/α + 1/β = -3/7

Thanks !!!


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