If (2x^3 + ax^2 + bx − 2) when divided by (2x − 3) and (x + 3) leaves remainders 7 and −20 respectively, find the values of a and b

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By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let, f(x) = 2x3 + ax2 + bx - 2. Given, Divisor : ⇒ 2x - 3 = 0 ⇒ 2x = 3 ⇒ x = Given, On dividing 2x3 + ax2 + bx - 2 by 2x - 3, remainder is 7. Divisor : ⇒ x + 3 = 0 ⇒ x = -3 On dividing 2x3 + ax2 + bx - 2 by x + 3, remainder is -20. ⇒ f(-3) = -20 ⇒ 2(-3)3 + a(-3)2 + b(-3) - 2 = -20 ⇒ 2(-27) + 9a - 3b - 2 = -20 ⇒ -54 + 9a - 3b - 2 = -20 ⇒ 9a - 3b - 56 = -20 ⇒ 9a - 3b = -20 + 56 ⇒ 9a - 3b = 36 ⇒ 3(3a - b) = 36 ⇒ 3a - b = ⇒ 3a - b = 12 ⇒ b = 3a - 12 ....(2) Substituting value of b from equation (2) in 3a + 2b = 3, we get : ⇒ 3a + 2(3a - 12) = 3 ⇒ 3a + 6a - 24 = 3 ⇒ 9a = 27 ⇒ a = ⇒ a = 3. Substituting value of a in equation (2), we get : ⇒ b = 3(3) - 12 ⇒ b = 9 - 12 ⇒ b = -3. Hence, the value of a = 3 and b = -3.

Mathematics

If (2x³ + ax² + bx - 2) when divided by (2x - 3) and (x + 3) leaves remainders 7 and -20 respectively, find values of a and b.

Factorisation

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If (2x3 + ax2 + bx - 2) when divided by (2x - 3) and (x + 3) leaves remainders 7 and -20 respectively, find values of a and b.

Factorisation

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