The expression 4x 3 - bx 2 + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

By remainder theorem, When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a). ⇒ x + 1 = 0 ⇒ x = -1 Given, 4x 3 - bx 2 + x - c leaves remainder 0 on dividing it by (x + 1). ∴ 4(-1) 3 - b(-1) 2 + (-1) - c = 0 ⇒ 4(-1) - b(1) - 1 - c = 0 ⇒ -4 - b - 1 - c = 0 ⇒ b + c = -5 ⇒ b = -5 - c .........(1) Given, 4x 3 - bx 2 + x - c leaves remainder 30 on dividing it by (2x - 3). 2x - 3 = 0 ⇒ 2x = 3 ⇒ x = Substituting x = in 4x 3 - bx 2 + x - c should give result as 30, Substituting value of b from (1) in above equation : ⇒ 60 - 9(-5 - c) - 4c = 120 ⇒ 60 + 45 + 9c - 4c = 120 ⇒ 5c + 105 = 120 ⇒ 5c = 120 - 105 ⇒ 5c = 15 ⇒ c = = 3. Substituting value of c in (1), we get : ⇒ b = -5 - c = -5 - 3 = -8. Hence, b = -8 and c = 3.

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

View Answer Bookmark Now

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.

View Answer Bookmark Now

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

View Answer Bookmark Now

Mathematics

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

Factorisation

Related Questions

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Mathematics

The expression 4x3 - bx2 + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

Factorisation

Related Questions

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

Show that 2x + 7 is a factor of 2x3 + 7x2 - 4x - 14. Hence, solve the equation :2x3 + 7x2 - 4x - 14 = 0.

What number should be subtracted from 2x3 - 5x2 + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :
2x³ + 7x² - 4x - 14 = 0.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?