Question

Given that the zeroes of the cubic polynomialx - 6x² + 3x + 10 are of the form a, a + b, a + 2b
for some real numbers 'a' and 'b'. Find the values of 'a' and 'b' as well as the zeroes of the given
polynomial​

Answer 1

Answer:   -1,2,5

Step-by-step explanation:

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