Question

Let p and q be the roots of the polynomial mx^2 + x(2 - m) + 3. Let m1 and m2 be two values of m satisfying p/q + q/p = 2/3. Determine numerical value of m1/(m2)^2 + m2/(m1)^2.

Answer 1

Answer:

m1/m2² + m2/m1² = 99

Step-by-step explanation:

p/q + q/p = 2/3

=> (p² + q²)/pq = 2/3

=> ( p+q)² - 2pq) /pq = 2/3

=> ( p+q)² - 2pq  = 2pq/3

=> ( p+q)² -8pq/3 = 0

mx² + x(2 - m) + 3

p + q  = -(2-m)/m = (m-2)/m  

pq = 3/m

=>( (m-2)/m)² - 8/m = 0

=> m² + 4 - 4m   - m = 0

=> m² - 12m + 4 = 0

m1 & m2 are roots

m1 + m2 = 12

m1.m2 = 4

m1/m2² + m2/m1²

= (m1³ + m2³)/(m1m2)²

m1³ + m2³ = (m1 + m2)³ - 3m1m2(m1+m2) =  (12)³  - 3*4*12 = 12 *12(12 - 1)

= 144 * 11

(m1m2)² = 4² = 16

m1/m2² + m2/m1² = 144 * 11/ 16 = 9 * 11 = 99

Answer 2

Answer:

Step-by-step explanation:

p/q + q/p = 2/3

=> (p² + q²)/pq = 2/3

=> ( p+q)² - 2pq) /pq = 2/3

=> ( p+q)² - 2pq  = 2pq/3

=> ( p+q)² -8pq/3 = 0

mx² + x(2 - m) + 3

p + q  = -(2-m)/m = (m-2)/m  

pq = 3/m

=>( (m-2)/m)² - 8/m = 0

=> m² + 4 - 4m   - m = 0

=> m² - 12m + 4 = 0

m1 & m2 are roots

m1 + m2 = 12

m1.m2 = 4

m1/m2² + m2/m1²

= (m1³ + m2³)/(m1m2)²

m1³ + m2³ = (m1 + m2)³ - 3m1m2(m1+m2) =  (12)³  - 3*4*12 = 12 *12(12 - 1)

= 144 * 11

(m1m2)² = 4² = 16

m1/m2² + m2/m1² = 144 * 11/ 16 = 9 * 11 = 99

pls mark the brainliest