You visited us 1 times! Enjoying our articles? Unlock Full Access!

Remainder Theorem

The polynomia...

Question

The polynomials ax³ + 3x² − 3 and 2x³ − 5x + a when divided by (x − 4) leave the remainders R₁ and R₂ respectively. Find the values of a in each of the following cases, if

(a) R₁ = R₂

(b) R₁ + R₂ = 0

(c) 2R₁ − R₂ = 0

Open in App

Solution

Let us denote the given polynomials as

Now, we will find the remaindersandwhenandrespectively are divided by.

By the remainder theorem, whenis divided bythe remainder is

By the remainder theorem, whenis divided bythe remainder is

(i) By the given condition,

R₁ = R₂

(ii) By the given condition,

R₁ + R₂ = 0

(iii) By the given condition,

2R₁ − R₂ = 0

Suggest Corrections

Similar questions

(2 x^{3} - 5 x^{2} + x + a)

(a x^{3} + 2 x^{3} - 3)

(x - 2)

R_{1}

R_{2}

^{'} a^{'}

2 R_{1} + R_{2} = 0

a x^{3} + 3 x^{2} - 3

2 x^{3} - 5 x + a

R_{1}

R_{2}

2 R_{1} - R_{2} = 0

-

-

-

-

The polynomial bx³+3x²-3 and 2x³-5x+b when divided by (x-4) leaves the remainders R₁ and R₂ respectively. Find the value of b if 2R₁-R₂=0

R_{1}

R_{2}

a x^{3} + 3 x^{2} - 3

2 x^{3} - 5 x + 2 a

2 R_{1} - R_{2} = 0

Join BYJU'S Learning Program