Question

3. If
$\alpha \: and \: \beta$

are the zeros of the quadratic polynomial f(x) = 6x² +x-
2, find the value of
$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha }$
​

Answer 1

Given :

• f ( x ) = 6x² + x - 2

To Find :

• α/β + β/α

Solution :

➨ 6x² + x - 2

By splitting middle term

➨ 6x² + 4x - 3x - 2

➨ 2x ( 3x + 2 ) - 1 ( 3x + 2 )

➨ ( 2x - 1 ) ( 3x + 2 )

➨ α = 1/2

➨ β = - 2/3

Put value of α and β in α/β + β/α

➨ ( 1/2 ) / ( -2/3 ) + ( - 2/3 ) / ( 1/2 )

➨ ( -3/4 ) + ( - 4/3 )

➨ ( - 9 - 16 ) / 12

➨ - 25 / 12

Answer 2

Answer:

α/β + β/α = -25/12

Step-by-step explanation:

f(x) = 6x^2 + x - 2

By splitting middle term method :

6x^2 + 4x - 3x - 2

= 2x ( 3x + 2 ) - 1 ( 3x + 2 )

= ( 2x - 1 ) ( 3x + 2 )

Here,

α = 1/2

β = - 2/3

Putting value of α and β in α/β + β/α

( 1/2 ) / ( -2/3 ) + ( - 2/3 ) / ( 1/2 )

= ( -3/4 ) + ( - 4/3 )

= ( - 9 - 16 ) / 12

= - 25 / 12

Hence,

α/β + β/α = -25/12

Ans...

Hope it helps you...

Mark it as Brainliest...