Let R 1 and R 2 are remainders when the polynomial x 3 + 2x 2 - 5ax - 7 and x 3 + ax 2 - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R 1 + R 2 = 6; find the value of a.

On dividing x 3 + 2x 2 - 5ax - 7 by (x + 1), we get remainder R 1 : ∴ R 1 = (-1) 3 + 2(-1) 2 - 5a(-1) - 7 ⇒ R 1 = -1 + 2 + 5a - 7 ⇒ R 1 = 5a - 6. On dividing x 3 + ax 2 - 12x + 6 by (x - 2), we get remainder R 2 ∴ R 2 = (2) 3 + a(2) 2 - 12(2) + 6 ⇒ R 2 = 8 + 4a - 24 + 6 ⇒ R 2 = 4a - 10. Given, ⇒ 2R 1 + R 2 = 6 ⇒ 2(5a - 6) + 4a - 10 = 6 ⇒ 10a - 12 + 4a - 10 = 6 ⇒ 14a - 22 = 6 ⇒ 14a = 28 ⇒ a = = 2. Hence, a = 2.

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Mathematics

Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.

Factorisation

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Mathematics

Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.

Factorisation

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Mathematics

Let R1 and R2 are remainders when the polynomial x3 + 2x2 - 5ax - 7 and x3 + ax2 - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R1 + R2 = 6; find the value of a.

Factorisation

Related Questions

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Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.

When 2x³ + 5x² - 2x + 8 is divided by (x - a) the remainder is 2a³ + 5a². Find the value of a.

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?