Math, asked by krishnasaraswat382, 3 months ago

if A and B are zeros of the polynomial 3 X square + 2 X + 3 then find One Upon A square + 1 upon B square​

Answers

Answered by BrainlyPhantom
20

Given polynomial

3x² + 2x + 3

[a = 3, b = 2, c = 3]

To find

1/α +1/β

Solution:

We know that in the polynomial ax² + bx +c,

α + β = -b/a

αβ = c/a

Substituting the values, we get:

-b/a = -2/3 = α + β

c/a = 3/3 = 1 = αβ

Now, we need to find 1/α +1/β. It can be written as:

\sf{\longrightarrow\:\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{\alpha+\beta}{\alpha\beta}}

Now, substituting the values, we get:

\sf{\longrightarrow\:\dfrac{-2}{3}\div1}

\bf{\longrightarrow\:\dfrac{-2}{3}}

The required answer is -2/3.

Knowledge Bytes:

For a polynomial ax² + bx +c, there will be two zeros - α and β. The sum of the zeros, α + β will be equal to -b/a (coefficients of the polynomial) and the product of zeros, αβ will be equal to c/a.


BrainlyPhantom: Thank you for the Brainliest :)
Answered by NewGeneEinstein
0

{\boxed{\sf Given}}

If α and β are zeroes of 3x² + 2x + 3

{\boxed{\sf To\;Find}}

1/α + 1/β

{\boxed{\sf Solution}}

Let us compare the given equation with the original form of the quadratic equation i.e ax² + bx + c

a = 3

b = 2

c = 3

1/α + 1/β

α + β/αβ

(-b/a)/(c/a)

(-2/3)/(3/3)

-2/3 × 3/3

-6/9

-2/3

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