CameraIcon

SearchIcon

MyQuestionIcon

1

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

thumbs-up

1

Similar questions

Q. The polynomials

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

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

when divided by

(x - 2)

leave the remainders

R_{1}

R_{2}

respectively. Find the value of

^{'} a^{'}

in the following case, if

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

Q. The polynomials

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

2 x^{3} - 5 x + a

when divided by (x - 4) leaves remainder

R_{1}

R_{2}

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

Q. R₁ and R₂ are the remainders when the polynomial ax³ + 3x^₂

-

-

5x + 2a are divided by (x

-

4) respectively. If 2R₁

-

R₂= 0, then find the value of a.

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}

are the reminders when the polynomial

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

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

are divided by (x-4) respectively. If

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

, then find the value of a

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Remainder Theorem

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Remainder Theorem

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon