Question

if alpha and beta are the zeroes of polynomial x^2+x-2 find the value of (1/alpha+1/beta)

Answer 1

$\boxed{\textbf{\large{Answer}}}$

(1/alpha+1/beta) = 1/ 2

Explanation :

☑ Given equation is x^2 + x - 2 equate the equation with zero

x^2 + x - 2 = 0

☑ Now find the roots of the equation

x^2 + 2x - x - 2 = 0

x ( x + 2) - 1( x + 2 ) = 0

( x + 2 ) ( x - 1 ) = 0

x = -2 OR x = 1

$\boxed{\textbf{\large{verification of roots}}}$

☑ First put x = - 2 in equation(x^2 + x - 2 = 0) and equate it with zero

((-2)^2 + (-2) - 2 = 0

((4)-4) = 0

0 = 0

Now, put x = 1 in the equation (x^2 + x - 2 = 0)

((1)^2 + 1 - 2 ) = 0

( 2 - 2 ) = 0

0 = 0

⚫Hence verified both the roots

☑ As a given α(alpha) and β(beta) are the roots of the quadratic equation

so, α = -2 and β = 1

we have to find

(1/alpha+1/beta) = 1/α + 1/β

= (1/(-2) ) +( 1 / 1)

= ( 1 / -2 ) + 1

= [ 1 + (-2) ] / (-2)

= (-1) / (-2)

= 1/ 2

⚫Therefor

(1/alpha+1/beta) = 1/ 2

Answer 2

Step-by-step explanation:

"If alpha and beta are the zeroes of the polynomial"

Taking this into account

1/alpha - 1/beta = 1/0 - 1/0

= infinity - infinity

which is not defined

if incase

"If alpha and beta are the solutions of the polynomial"

x^2 + x - 2 =0

(x+2)(x -1) = 0

=> x= -2 or x =1

therefore (alpha,beta) = (1,-2) or (-2,1)

1/alpha - 1/beta = +(3/2) or -(3/2)