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