Question

find the value of a,if (x-a) is afactor of x^3-ax^2+x+2

Answer 1

since , ( x-a ) is a factor of x³-ax²+x+2

=> f (x) = x³-ax²+x+2

=> ( x-a ) = 0

=> x = a

according to factor theorem ,

f ( a ) = 0

=> f ( a ) = a²-a (a²)+a+2

=> 0 = a³ - a³ + a + 2

=> 0 = a + 2

=> a = -2


hope this helps

Answer 2

As we know x-a is the factor of x³-ax²+x+2
So, x-a=0
Then, x=a

Now putting the value of x=a in x³-ax²+x+2

= (a)³-a(a)²+(a)+2=0

a³-a³+a+2=0

a+2=0

a= -2

Hope this helps you