If a x⁴+b x³+c x²+d x+e= | array ccc x³+3 x & x-1 & x+3 x+1 & -2 x & x-4 x-3 & x+4 & 3 x array | , then e is equal to

Step-by-step solution

Given, a x⁴+b x³+c x²+d x+e = | array ccc x³+3 x & x-1 & x+3 x+1 & -2 x & x-4 x-3 & x+4 & 3 x array | On putting x=0 both sides, we get e= | array rrr 0 & -1 & 3 1 & 0 & -4 -3 & 4 & 0 array | Expanding along first row, we get aligned &=0(0+16)-(-1)(0-12)+3(4-0) &=0-12+12=0 aligned