Question 3 :: The Value of a for Which (X+ A) is a factor of the polynomial X.X.X + A.X.X – 2X + A + 6 is (X cube plus A into X square minus 2x plus A plus 6 is)
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Step-by-step explanation:
+a
x
x
x
x+a
x
x
x
x+a
∣
∣
∣
∣
∣
∣
∣
∣
=0
Applying R
1
=R
1
−R
2
,R
2
=R
2
−R
3
∣
∣
∣
∣
∣
∣
∣
∣
a
0
x
−a
a
x
0
−a
x+a
∣
∣
∣
∣
∣
∣
∣
∣
=0
Taking a common from first and second row respectively
⇒a
2
∣
∣
∣
∣
∣
∣
∣
∣
1
0
x
−1
1
x
0
−1
x+a
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒
∣
∣
∣
∣
∣
∣
∣
∣
1
0
x
−1
1
x
0
−1
x+a
∣
∣
∣
∣
∣
∣
∣
∣
=0,∵a
=0
Now expanding along first row we get,
1(x+a+x)+1(0+x)=0
⇒3x+a=0⇒x=−
3
a
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