given that 6x^3+5a-12a leaves a remainder of -4 when divided by (x-a). what will be the possible value of a ?
Assuming a typo, we have
f(a) = 6a^3+5a^2-12a = -4
6a^3+5a^2-12a+4 = 0
(a+2)(2a-1)(3a-2) = 0
. . .
To find the possible value of 'a', we need to use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by (x-a), then the remainder is equal to f(a).
In this case, the polynomial 6x^3 + 5a - 12a leaves a remainder of -4 when divided by (x-a). So, substituting x = a into the polynomial, we can set it equal to the remainder:
6a^3 + 5a - 12a = -4
Simplifying this equation:
6a^3 - 7a = -4
Rearranging the terms:
6a^3 - 7a + 4 = 0
This is a cubic equation. To find the possible values of 'a', we can either solve this equation analytically or use a calculator to find the roots.
To find the possible value of 'a' that satisfies the given condition, we need to use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x - a), where 'a' is a constant, then the remainder is equal to f(a).
In this case, we are given that the polynomial 6x^3 + 5a - 12a leaves a remainder of -4 when divided by (x - a). So, we can set up the following equation:
6a^3 + 5a - 12a = -4
Simplifying this equation:
6a^3 - 7a = -4
Now, let's solve this equation to find the possible values of 'a'.