Q. 3 B5.0( 4 Votes )
Applying Remainder Theorem, let us write the remainders, when,
the polynomial x3 – ax2 + 2x – a is divided by (x – a)
Answer :
Remainder theorem says that,
f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).
Let us solve the following questions on the basis of this remainder theorem.
Let f(x) = x3 – ax2 + 2x – a …(1)
When x3 – ax2 + 2x – a is divided by (x – a).
Now, let’s find out the zero of the linear polynomial, (x – a).
To find zero,
x – a = 0
⇒ x = a
This means that by remainder theorem, when x3 – ax2 + 2x – a is divided by (x – a), the remainder comes out to be f(a).
From equation (1), remainder can be calculated as,
Remainder = f(a)
⇒ Remainder = (a)3 – a(a)2 + 2(a) – a
⇒ Remainder = a3 – a3 + 2a – a
⇒ Remainder = 2a – a
⇒ Remainder = a
∴ the required remainder = a
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