If p(x)=x* + ax + bx² +cx+d and p(1...
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If p(x)=x* + ax + bx² +cx+d and p(1)=p(2)=P(3)=0 , then the value if p(4)+(0) = ......... (A) 10 (B) 24 (C) 25 (D) 12

JEE/Engineering Exams
Maths
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p(x) =x4+ax3+bx2+cx+da p(1)=p(2)=p(3)=0 1+a+b+c+d=0           ......1 16+sa+4b+2c+d=0    ......2 81+27a+9b+3c+d=0   .....3 subtract (2) & 1 15+7a+3b+c=0 subtract (3) & (2) 65+19a+5b+c=0   ....(5) subtract (4) & (5)   50+12a+2b=0 6a+b=-25 Now, p(4)+p(0)=256+64a+16b+4c+d+d =256+64a+16b+4c+2d =(175+37a+7b+c+d)+(81+27a+9b+3c+d) =175+37a+7b+c+d =174+36a+6b+1+a+b+c+d =174+36a+6b =174+6(6a+b) =174-6×25=174-150 =24 Ans. (b)

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