Math, asked by venu77421234, 6 months ago

find a and b,if (x+1)and(x+2) are factors of x^3+3x^2-2ax+b​

Answers

Answered by amansharma264
10

EXPLANATION.

( x + 1 ), ( x + 2 ) are the factor of x³ + 3x² - 2ax + b.

To find the value of a and b.

CASE = 1.

→ x + 1 = 0

→ x = -1

Put the value of x = -1 in equation.

→ (-1)³ + 3(-1)² - 2a(-1) + b = 0.

→ -1 + 3 + 2a + b = 0.

→ 2a + b + 2 = 0.

→ b = -2 - 2a .............(1)

CASE = 2.

→ x + 2 = 0.

→ x = -2.

Put the value of x = -2 in equation

→ (-2)³ + 3(-2)² - 2a(-2) + b = 0.

→ -8 + 12 + 4a + b = 0.

→ 4 + 4a + b = 0 ......(2)

Put the value of equation (1) in equation (2)

we get,

→ 4 + 4a + ( - 2 - 2a ) = 0.

→ 4 + 4a - 2 - 2a = 0.

→ 2 + 2a = 0

→ a = -1.

Put the value of a = -1 in equation (1)

we get,

→ b = -2 - 2(-1).

→ b = -2 + 2

→ b = 0.

VALUE OF A = -1 AND B = 0.


Glorious31: Great !
amansharma264: Thanku
Answered by Anonymous
8

\sf{Answer}

Step by step explanation:-

Given :-

Q.E = x³+3x²-2ax + b

Factors of Q.E

  • x+1
  • x +2

To find :-

Values of a,b

Solution:-

As they given Factors.

So,

x + 1 = 0

x = -1

Substuite x= -1 in given equation

x³+3x²-2ax + b =0

(-1)³ +3 (-1)² -2(a)(-1) +b =0

-1 +3 +2a + b = 0

2a + b + 2 =0 _______ eq 1

Another factor,

x +2 =0

x = -2

Substuite x = -2 in given Equation

x³+3x²-2ax + b = 0

(-2)³ + 3(-2)² -2(a)(-2) + b = 0

-8 + 12 + 4a + b =0

4 + 4a + b =0

4a + b + 4 = 0 _______ eq 2

Subtract eq 1 from eq2

2a + b + 2 =0

4a + b + 4 = 0

____________

Change the signs

Since ,

-2a -2 =0

-2a = 2

a = -1

Substuite value of a in eq 1

2a + b + 2 =0

2(-1) + b + 2 =0

-2 + b +2 =0

-2 +2 +b =0

b =0

Required answer :-

Values of a,b are. -1,0

_______________________________

Hope my answer helps to u

Thank u :)

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