Question

If a.ß are the zeroes of the polynomial 3x^2 + 8x+2, then 1/a +1/ß
is​

Answer 1

Answer :

The required value is -4

Given :

The zeroes of the polynomial

3x² + 8x + 2 are :

$\alpha \: \: and \: \: \beta$

Concept to be used :

$\bullet \: \: \rm Sum \: of \: the \: zeroes = - \dfrac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$\bullet \: \: \rm Product \: of \: the \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} }$

To Find :

The value of

$\rm \dfrac{1}{\alpha}+\dfrac{1}{\beta}$

Solution :

The quadratic polynomial is

3x² + 8x + 2

From the sum relation we have ,

$\rm \implies \alpha + \beta = -\dfrac{8}{3} \longrightarrow (1)$

Now from product relation,

$\rm \implies \alpha \beta=\dfrac{2}{3} \longrightarrow(2)$

Dividing (1) by (2) we have,

$\rm \implies \dfrac{\alpha + \beta}{\alpha\beta}=\dfrac{-\dfrac{8}{3}}{\dfrac{2}{3}}\\\\ \implies \dfrac{\alpha}{\alpha\beta}+\dfrac{\beta}{\alpha\beta}=-\dfrac{8}{2}\\\\ \implies \dfrac{1}{\alpha}+\dfrac{1}{\beta}= -4$

Answer 2

Answer:

Step-by-step explanation:

Equation is 3x² + 8x + 2

On comparing this equation ,

a = 3 , b = 8 , c = 2

sum of zeroes = -b /a

alpha + beta = -8/3

product of zeroes = c/a

alpha × beta = 2/3

alpha ² + beta² = (alpha + beta ) ² - 2alpha× beta

( -8/3)² - 2 × 2/3

64/9 - 4/3

52/9

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