The polynomials ax 3 + 3x 2 - 3 and 2x 3 - 5x + a when divided by x - 4 leave the remainder r 1 and r 2 respectively. If 2r 1 = r 2 , then find the value of a.

By remainder theorem, on dividing f(x) by (x - b), remainder = f(b) ∴ On dividing, f(x) = ax 3 + 3x 2 - 3 by (x - 4) Remainder = f(4) = a(4) 3 + 3(4) 2 - 3 = 64a + 45 ∴ On dividing, f(x) = 2x 3 - 5x + a by (x - 4) Remainder = f(4) = 2(4) 3 - 5(4) + a = 128 - 20 + a = 108 + a According to question, r 1 = 64a + 45 r 2 = 108 + a 2r 1 = r 2

When divided by x - 3 the polynomials x³ - px² + x + 6 and 2x³ - x² - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

View Answer Bookmark Now

Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

View Answer Bookmark Now

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

View Answer Bookmark Now

By factor theorem, show that (x + 3) and (2x - 1) are the factors of 2x² + 5x - 3.

View Answer Bookmark Now

Mathematics

The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the remainder r₁ and r₂ respectively. If 2r₁ = r₂, then find the value of a.

Factorisation

Related Questions

When divided by x - 3 the polynomials x³ - px² + x + 6 and 2x³ - x² - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

By factor theorem, show that (x + 3) and (2x - 1) are the factors of 2x² + 5x - 3.

Mathematics

The polynomials ax3 + 3x2 - 3 and 2x3 - 5x + a when divided by x - 4 leave the remainder r1 and r2 respectively. If 2r1 = r2, then find the value of a.

Factorisation

Related Questions

When divided by x - 3 the polynomials x3 - px2 + x + 6 and 2x3 - x2 - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

Find 'a' if the two polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.

Using the remainder theorem, find the remainders obtained when x3 + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

By factor theorem, show that (x + 3) and (2x - 1) are the factors of 2x2 + 5x - 3.

The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the remainder r₁ and r₂ respectively. If 2r₁ = r₂, then find the value of a.

When divided by x - 3 the polynomials x³ - px² + x + 6 and 2x³ - x² - (p + 3)x - 6 leave the same remainder . Find the value of 'p'.

Find 'a' if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of two remainders is 1.

By factor theorem, show that (x + 3) and (2x - 1) are the factors of 2x² + 5x - 3.