Question

If alpha and beta are the zeros of the polynomial p(x)= 4xsquare - 2x - 3 find the value of 1/alfa + 1/beta

Answer 1

Answer:

- 2 / 3

Step-by-step explanation:

Given----> α and β are the zeroes of the polynomial P ( x ) = 4x² - 2x - 3 .

To find---> find the value of ( 1 / α + 1 / β )

Solution---> ATQ,

P( x ) = 4x² - 2x - 3

Zeroes of above polynomial are α and β .

We know that ,

Sum of zeroes = - Coefficient of x/Coefficient of x²

=> α + β = - ( - 2 ) / 4

=> α + β = 1 / 2

Product of zeroes

= Constant term/Coefficientof x²

=> α β = -3 / 4

Now,

1 / α + 1 / β = ( α + β ) / αβ

= ( 1 / 2 ) / ( -3 / 4 )

= - 4 / 6

= - 2 / 3

Answer 2

Answer:

Step-by-step explanation:

Given----> α and β are the zeroes of the polynomial P ( x ) = 4x² - 2x - 3 .

To find---> find the value of ( 1 / α + 1 / β )

Solution---> ATQ,

P( x ) = 4x² - 2x - 3

Zeroes of above polynomial are α and β .

We know that ,

Sum of zeroes = - Coefficient of x/Coefficient of x²

=> α + β = - ( - 2 ) / 4

=> α + β = 1 / 2

Product of zeroes

= Constant term/Coefficientof x²

=> α β = -3 / 4

Now,

1 / α + 1 / β = ( α + β ) / αβ

= ( 1 / 2 ) / ( -3 / 4 )

= - 4 / 6

= - 2 / 3