If (x-2) is a factor of x^3 - 4x^2 +ax+b and x^3 -ax^2 +bx + 8, then the values of a and b are respectively
1. 3 and 5
2. 2 and -4
3. 4 and 0
4. 0 and 4
Answers
Answered by
2
Step-by-step explanation:
x-2
=> x= 2
NOW PUT THE VALUE OF X IN BOTH THE EQUATION.
FIRST EQUATION,
x³-4x²+ax+b=0
=> 2³-4(2)²+a(2)+b=0
=> 8-4(4)+ 2a +b=0
=>. 8-16+2a+b=0
=>. -8+2a+b=0
=>. 2a+b-8=0 ---------- 1
SECOND EQUATION,
x³-ax²+bx+8=0
=> 2³-a(2)²+b(2)+8=0
=>. 8- 4a+ 2b +8=0
=>. -4a+2b+16=0 --------2
BY SUBSTITUTION METHOD,
FROM 1,
a= 8-b/2 ---------3
SUBSTITUTE 3 ON 2,
-4(8-b/2) +2b+16=0
=> -2(8-b)+2b+16=0
=>. -16+2b+2b+16=0
=>. 4b-0=0
=>. b=0/4
=>. b=0
SUBSTITUTE VALUE OF b ON 3,
a= 8-b/2
a= 8-0/2
a= 8/2
a= 4
HENCE, a= 4 and b= 0
SO, option iii is correct.
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