The expression 2x 3 + ax 2 + bx - 2 leaves remainder 7 and 0 when divided by 2x - 3 and x + 2 respectively. Calculate the values of a and b.

2x - 3 = 0 ⇒ x = Given, when 2x 3 + ax 2 + bx - 2 is divided by 2x - 3, the remainder is 7. ∴ On substituting x = in 2x 3 + ax 2 + bx - 2 , remainder = 7. x + 2 = 0 ⇒ x = -2 Given, when 2x 3 + ax 2 + bx - 2 is divided by x + 2, the remainder is 0. ∴ On substituting x = -2 in 2x 3 + ax 2 + bx - 2 , remainder = 0. ⇒ 2(-2) 3 + a(-2) 2 + b(-2) - 2 = 0 ⇒ 2(-8) + 4a - 2b - 2 = 0 ⇒ -16 + 4a - 2b - 2 = 0 ⇒ 4a - 2b - 18 = 0 Substituting value of 2b from (i) in above equation, ⇒ 4a - (3 - 3a) - 18 = 0 ⇒ 4a + 3a - 18 - 3 = 0 ⇒ 7a = 21 ⇒ a = 3. Substituting value of a in (i) we get, ⇒ 2b = 3 - 3(3) ⇒ 2b = 3 - 9 ⇒ 2b = -6 ⇒ b = -3. Hence, a = 3 and b = -3.

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

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When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

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(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

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Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.

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Mathematics

The expression 2x³ + ax² + bx - 2 leaves remainder 7 and 0 when divided by 2x - 3 and x + 2 respectively. Calculate the values of a and b.

Factorisation

Related Questions

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.

Mathematics

The expression 2x3 + ax2 + bx - 2 leaves remainder 7 and 0 when divided by 2x - 3 and x + 2 respectively. Calculate the values of a and b.

Factorisation

Related Questions

The polynomial px3 + 4x2 - 3x + q is completely divisible by x2 - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x3 + 2x2 - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x3 + ax2 - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x3 + (a + 1)x2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2) leaves a remainder 7.

The expression 2x³ + ax² + bx - 2 leaves remainder 7 and 0 when divided by 2x - 3 and x + 2 respectively. Calculate the values of a and b.

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.