Question

Find k so that x²+2x+k is factor is 2x⁴+x³-14x²+5x+6.Also, find all the zeroes of the two polynomials.

Answer 1

${x}^{2} + 2x + k = 0 \\ by \: trial \:method 1 \: 2 \: 3 \\ {1}^{2} + 2(1) + k = 0 \\ 1 + 2 + k = 0 \\ 3 + k = 0 \\ k = - 3 \\ \\p({x}) = 2 {x}^{4} + {x}^{3} - 14 {x }^{2} + 5x + 6 = 0 \\ by \: trial \: method \: 1 \: 2 \: 3 \\ 2( {1})^{4} + {1}^{3} - 14( {1})^{2} + 5(1) + 6 = 0 \\ 2(1) + 1 - 14(1) + 5 + 6 = 0 \\ 2 + 1 - 14 + 5 + 6 = 0 \\ 3 - 14 + 11 = 0 \\ - 11 + 11 = 0 \\ 0 = 0$
${x}^{2} + 2x + k = 0\\ by \: trial \: method \: 1\: 2 \: 3 \\ {1}^{2} + 2(1) + k = 0 \\ 1 + 2 + k = 0 \\ 3 + k = 0 \\ k = - 3$
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