Question

23. Given that the zeroes of the cubic polynomial
x^3 - 6x^2 +3x +10
are of
form a, a+b, a+ 2ab for
some real numbers a and b
find the values of a & b as well as the zeroes of the given
the polynom
ial​

Answer 1

Polynomial = x^3 - 6x^2 +3x +10

Zeroes = a, a+b, a+ 2ab

P(-1) = -1^3 -6(-1)^2 + 3(-1) +10

= -1 -6 -3+10

=-10+10

= 0

Therefore x = -1

and (x+1) is a factor of given p(x)

dividing (x+1) We get

f(x) = x^2 - 7x +10

f(x) = x^2 - 5x-2x+10

f(x) = x(x-5) -2 (x-5)

f(x) = (x-2)(x-5)

Therefore values of x = 2,5 ,-1

» a = -1

» a+b = 2 or, b = 3

»a+2b = 5

Values a = -1 and b = 3