Show that 2x + 7 is a factor of 2x 3 + 7x 2 - 4x - 14. Hence, solve the equation : 2x 3 + 7x 2 - 4x - 14 = 0.

Given, ⇒ 2x + 7 = 0 ⇒ 2x = -7 ⇒ x = - Substituting x = - in L.H.S. of 2x 3 + 7x 2 - 4x - 14 = 0, we get : Since, L.H.S. = R.H.S. = 0. ∴ 2x + 7 is a factor of 2x 3 + 7x 2 - 4x - 14 = 0. Dividing 2x 3 + 7x 2 - 4x - 14 = 0 by 2x + 7: ∴ 2x 3 + 7x 2 - 4x - 14 = (2x + 7)(x 2 - 2) = (2x + 7)(x + ) Solving, ⇒ 2x + 7 = 0 ⇒ 2x = -7 ⇒ x = - Also, ⇒ x + = 0 ⇒ x = - = -1.41 Also, ⇒ x - = 0 ⇒ x = = 1.41 Hence, x = -, 1.41, -1.41

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

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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.

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Mathematics

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

Factorisation

Related Questions

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.

Mathematics

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

Factorisation

Related Questions

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 ?

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.