Question

if alpha and beta are the zeroes of the polynomial 3x² -4x +5 then find the value of alpha/beta+beta/alpha​

Answer 1

Answer:

alpha/beta + beta/alpha = -14/15

Step-by-step explanation:

p(x) = 3x^2 - 4x + 5

Here,

a = 3 , b = -4 , c = +5

Let the zeroes of the polynomial be

'alpha' and 'beta'. Then,

We know that,

alpha + beta = -b/a

=> alpha + beta = -(-4)/3

=> alpha + beta = 4/3 ...(1)

Also,

(alpha)(beta) = c/a

=> (alpha)•(beta) = 5/3 ...(2)

Now according to the question,

alpha/beta + beta/alpha =

= {(alpha)^2+(beta)^2}/ {(alpha)(beta)}

we know that,

a^2 + b^2 = (a+b)^2 - 2ab

Applying this identity in the equation, we get

= {(alpha+beta)^2 - 2•(alpha)•(beta)} /

{ (alpha)•(beta) } ...(3)

From eq. (1) , eq.(2) and eq.(3) ,we get,

= {(4/3)^2 - 2(5/3)} / (5/3)

= { 16/9 - 10/3 } / (5/3)

= { (16 - 30)/9} / (5/3)

= (-14/9) / (5/3)

= (-14×3) / (9×5)

= (-14) / (3×5)

= -14/15

Hence,

alpha/beta + beta/alpha = -14/15