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प्रश्न
Solve the equation 9x3 – 36x2 + 44x – 16 = 0 if the roots form an arithmetic progression
उत्तर
Given the roots are in AP
Let the roots be a – d, a, a + d
Sum of the roots
a − d + a + a + d = `36/9` = 4
3a = 4
a = `4/3`
Product of the roots
(a – d) a (a + d) = `16/9`
(a2 – d2)a = `16/9`
`16/9 - "d"^2 = 4/3`
`16/9 - 4/3` = d2
d2 = `(16 - 12)/9 = 4/9`
d = `2/3`
∴ a – d = `4/3 - 2/3 = 2/3`
a + d = `4/3 + 2/3 = 6/3` = 2
Roots are a – d, a, a + d be `2/3, 4/3, 2`.
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