Question

6. If f(x) = x 3+ x2- ax + b is divisible by x2- x, then find the value of a and b

Answer 1

Answer:

x3+x2-ax+B is divisible by x2-x so tis mean that reminder will be zero when it will be divided by x2-x

when you divide x3+x2-ax+B by x2-x you get a remainder

remainder =o , equate the like power of x you get the value of a,b

Answer 2

Answer:

a = -2 ; b = 0.

Step-by-step explanation:

Consider the factor of the given equation to be 0.

$x {}^{2} - x = 0 \\ x(x - 1) = 0 \\ x = 0 \: or \: x = 1$

Then, when x = 0;

$f(x) = x {}^{3} + x {}^{2} - ax + b \\ f(x) = 0 \: ,when \: x = 0 \\ f(0) = 0 {}^{3} + 0 {}^{2} - a \times 0 + b = 0\\ b = 0$

when x = 1;

$f(x) = x {}^{3} + x {}^{2} - ax + b \\ f(x) = 0 \: ,when \: x = 1 \\ f(1) = 1 {}^{3} + 1 {}^{2} + a \times 1 + b = 0$

$(b = 0) \\ f(1) = 1 + 1 + a + 0 = 0 \\ a = - 2$

Hence, a = -2 ; b = 0.

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Hope it helps....!

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