Question

if 3 is the zero of p(x)=x raise to the power 4 - 3x raise to the power 3 - 7x raise to the power 2 + 15x +k find k.

Answer 1

x⁴ - 3x³ -7x² + 5x + k = 0 ( Subs. the zero i.e 3 ) 3⁴ -3*3³ -7*3²+ 5*7+k = 0 81- 3*27 - 7*9 + 35 + k = 0 81 - 81 - 63 + 35 + k = 0 -28 + k = 0 ∴ k = 28