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.

Question

Arun · 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

SAMBHAV MISHRA · Answer

@arun YOU COPIED THE ANSWER FROM BRAINLY.COM... IF I CAN GET THE ANSWER FROM THERE THEN WHAT IS THE USE OF COMING HERE....NOT EXPECTED

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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.

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.

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.

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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.

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.

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.

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