Math, asked by lucifer555, 1 year ago

If (x-2) is a factor of the expression 2xcube+axsquare+bx-14 and when the expression is divided by (x-3), it leaves a remainder 52, find the values a and b.

Attachments:

Answers

Answered by mysticd
77
I hope this helps you .

:)
Attachments:
Answered by amansharma264
5

EXPLANATION.

⇒ (x - 2) is a factor of the equation.

⇒ 2x³ + ax² + bx - 14.

As we know that,

⇒ (x - 2) is a factor of equation.

⇒ x - 2 = 0.

⇒ x = 2.

Put the value of x = 2 in the equation, we get.

⇒ 2(2)³ + a(2)² + b(2) - 14 = 0.

⇒ 16 + 4a + 2b - 14 = 0.

⇒ 4a + 2b + 2 = 0.

⇒ 2a + b + 1 = 0. - - - - - (1).

When the expression is divided by (x - 3) it leaves remainder 52.

As we know that,

⇒ (x - 3) is a factor of the equation.

⇒ x - 3 = 0.

⇒ x = 3.

Now, we can write equation as,

⇒ 2x³ + ax² + bx - 14 = 52.

⇒ 2(3)³ + a(3)² + b(3) - 14 = 52.

⇒ 54 + 9a + 3b - 14 = 52.

⇒ 9a + 3b + 40 = 52.

⇒ 9a + 3b + 40 - 52.

⇒ 9a + 3b - 12 = 0. - - - - - (2).

⇒ 3a + b - 4 = 0. - - - - - (2).

From equation (1) and (2), we get.

⇒ 2a + b + 1 = 0. - - - - - (1).

⇒ 3a + b - 4 = 0. - - - - - (2).

Subtract both the equation, we get.

⇒ 2a + b + 1 = 0. - - - - - (1).

⇒ 3a + b - 4 = 0. - - - - - (2).

⇒ -    -     +

We get,

⇒ - a + 5 = 0.

⇒ a = 5.

Put the values of a = 5 in the equation (1), we get.

⇒ 2a + b + 1 = 0.

⇒ 2(5) + b + 1 = 0.

⇒ 10 + b + 1 = 0.

⇒ b + 11 = 0.

⇒ b = - 11.

Values of a = 5  and  b = - 11.

Similar questions