Question

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
​

Answer 1

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.