Question

If α,β are 2 zeroes of the polynomial 4x^2 + 3x + 7, then 1/α + 1/β is equal to?

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

$itzDopeGirl$❣

Answer 2

Hey dear !!!

___________________________

==> 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 ,

1/α + 1/β

So, lets find this,

We have the following values ,as

a = 4

b = 3

c = 7

We know that,

α + β = -b/a

= -3/4

Also we know that,

αβ = c/a

= 7/4

Now, by using the identity of quadratic expression ,[ 1/α + 1/β = α+β/αβ ]

By putting the obtained value we get,

1/α + 1/β = α+β/αβ

= -3/4/74

4 and 4 get cancelled and we get

= -3/7

Therefore 1/α + 1/β = -3/7

 

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