Question

find the zeros of the polynomial X ^ 3 - 6 x ^ 2 + 3x + 10 it is given that the zeros are in A.P.
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Answer 1

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Using factorisation method,

a2-5a+a-5 = 0 =3

⇒ a (a – 5) + 1 (a – 5) = 0

⇒ (a – 5) (a + 1) = 0

⇒ a = -1, 5

when a = -1, then b = 3

When a = 5, then b = - 3 [using Eq. (i)]

∴Required zeroes of f(x) are

When a = -1 and b = 3

then, a,(a+b),(a + 2) = -1, (-1+3), (-1+6) or -1,2, 5

When, a = 5 and b = -3 then

a, (a + b), (a + 2b) = 5, (5 -3), (5 -6) or 5,2,-1.

Hence, the required values of a and b are a = – 1 and d = 3 or a = 5, b = -3 and the zeroes are -1,2 and 5.