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Q. If (x - 2) and (x - 3) are factors of a polynomial x3+ax2+bx+6, find a and b.

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Solution

Dear student
Given: x-2 and x-3 are factors of fx=x3+ax2+bx+6f2=0=f3f2=23+a22+2b+6=8+4a+2b+6=4a+2b+14So, 4a+2b+14=04a+2b=-14 2a+b=-7b=-7-2a ...1and f3=33+a32+3b+6=27+9a+3b+6=9a+3b+33So, 9a+3b+33=09a+3b=-33 3a+b=-113a-7-2a=-11 [using 1]a=-4and b=-7-2(-4)=-7+8=1So, a=-4 and b=1
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