If (x+2) and (x-1) are factors of the polynomial p(x)=x3+10x2+mx+n then (a) m=5,n=−3 (b) m=7,n=−18 (c) m=17,n=−8 (d) m=23,n=−19
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Solution
ANSWER: (b) m = 7, n = −18 Let: px=x3+10x2+mx+n Now, x+2=0⇒x=-2 (x + 2) is a factor of p(x). So, we have p(-2)=0 ⇒-23+10×-22+m×-2+n=0⇒-8+40-2m+n=0⇒32-2m+n=0⇒2m-n=32 ...i Now,