Find the zeros of ploynomial x3-6x2+4x-3
Answers
Step-by-step explanation:
If the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a,a + b and 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. 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.