Find-the-value-of-m-for-which-the-roots-of-the-equation-x-3-6x-2-11x-m-0-form-a-linear-sequence-

Question Number 95373 by Don08q last updated on 24/May/20

Find the value of m for which the roots

of the equation x^{3} + 6 x^{2} + 11 x + m = 0

form a linear sequence .

Commented by Rasheed.Sindhi last updated on 24/May/20

Linear sequence means AP ?

Commented by Don08q last updated on 24/May/20

Yes please

Answered by prakash jain last updated on 24/May/20

Let roots be a - d, a, a + d

sum of roots = - (coefficient of x^{2})

a - d + a + a + d = - 6 \Rightarrow a = - 2

sum of product of roots taken 2 at time

= + (coefficient of x)

(a - d) (a) + a (a + d) + (a - d) (a + d) = 11

2 a^{2} + a^{2} - d^{2} = 11

3 a^{2} - d^{2} = 11

d^{2} = 3 \times 4 - 11 = 1

product of roots = - (constant term)

m = - (a - d) (a) (a + d)

= - (a^{2} - d^{2}) a

= - (4 - 1) \times 6

Commented by Don08q last updated on 24/May/20

Please check again . a will be - 2

Commented by prakash jain last updated on 24/May/20

Corrected . forgot to divide