In the equation x^2+kx+54=0 one root is twice the other root find k
1 answer:
Let r be the lesser root and r^2 be the greater.......the sum of the roots = -b/a = -[-6] / 1 = 6
So we have that
r^2 + r = 6 → r^2 + r - 6 = 0
Factor
(r + 3) (r - 2) = 0
So r = -3 or r = 2
Then r^2 = 9 or r^2 =4
And the product of the roots = c/a = k/a = k
So....k = (-3)(9) = -27 or k = (2)(4) = 8
Check
x^2 - 6x - 27 = 0 factors as (x + 3)(x - 9) = 0 and the roots are -3 and 9
x^2 - 6x + 8 = 0 factors as (x -2) (x - 4) =0 and the roots are 2 and 4
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Step-by-step explanation:
First term [ a ] = 6.3
Common difference [ d ] = 8.8 - 6.3 = 2.5
Using general term formula,

78.8 = 6.3 + (n-1)*2.5
2.5*(n-1) = 72.5 [ Dividing both sides by 2.5 ]
n-1 = 29
n = 30
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Step-by-step explanation:
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