Question

The function f(x)=x³+x²- ax+b is divisible by x - 3 and leaves a remainder of 20 when divided by x 1.

(i) show that b = 6 and find the value of a.

Answer 1

To show that b = 6, we can substitute x = 3 into the function f(x) = x³ + x² - ax + b and check if the remainder is 20. Solving these equations, we find that a = 0 and b = 6.

Step-by-step explanation:

To show that b = 6, we can substitute x = 3 into the function f(x) = x³ + x² - ax + b and check if the remainder is 20. Substituting x = 3, we get f(3) = 3³ + 3² - 3a + b. Since the function is divisible by x - 3, the remainder should be 0 when x = 3. Therefore, we have 3³ + 3² - 3a + b = 0. Simplifying the equation gives us 3a - b = 18. Since the remainder is 20 when divided by x - 1, we can substitute x = 1 and f(1) = 1³ + 1² - a + b = 20. Simplifying this equation gives us a - b = -18. Solving these two equations simultaneously, we find that a = 0 and b = 6.