Solve this its urgent
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Solution!!
(x - 2) is a factor of (x³ + ax² + bx + 6)
x - 2 = 0
x = 2
f(x) = x³ + ax² + bx + 6
f(2) = (2)³ + a(2)² + b(2) + 6
0 = 8 + 4a + 2b + 6
0 = 14 + 4a + 2b
-14 = 4a + 2b
-7 = 2a + b...(i)
(x - 3) leaves a remainder 3
x - 3 = 0
x = 3
f(x) = x³ + ax² + bx + 6
f(3) = (3)³ + a(3)² + b(3) + 6
3 = 27 + 9a + 3b + 6
3 = 33 + 9a + 3b
3 - 33 = 9a + 3b
-30 = 9a + 3b
-10 = 3a + b...(ii)
On solving (i) and (ii), we get, (steps shown in the attachment)
a = -3
Putting the value of a in (i), we get,
-7 = 2a + b
-7 = 2(-3) + b
-7 = -6 + b
-7 + 6 = b
b = -1
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