Question

if m and n are the zeroes of x2 + 5x + 6 then the value of m2n + mn2 is a.5/6 b.11/30 c.6/5 d.-5/6​

Answer 1

Answer:

-30

Step-by-step explanation:

Given polynomial,

x² + 5x + 6

Comparing it with ax²+bx+c,we get a =1, b= 5, c= 6

Given, its zeros are m and n

Thus, m+n = -b/a and mn = c/a

or m+n = -5 and mn = 6

Cubing both sides,

(m+n)³ = (-5)³

or m³ + n³ +3 m²n + 3 m n² = -125 ...........(1)

Use the identity,

m³+n³ = (m+n)(m²+n²-m n)

or m³+n³ = (m+n){(m+n)²-3mn}

or m³+n³ = (-5){(-5)²-3(6)}

or m³+n³ = (-5)(25-18)

or m³+n³ = (-5)(7) = -35

Substituting in equation (1),

-35 + 3(m²n+mn²) = -125

or 3(m²n+mn²) = -90

or m²n + mn² = -30

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