Question

V3, find other zeroes.
6.) If the polynomial x4 – 6x' + 16x” – 25x + 10 is divided by another polynomial x - 2x + k,
the remainder comes out to be x + a, find kand a.​

Answer 1

$ANSWER</p><p></p><p>f(x)= is divided by another polynomial</p><p>x2−2x+k)x4−6x3+16x2−25x+10(x2−4x+(8−k)</p><p>                       −x4+−2x3−+kx2</p><p>                       −4x3+(16−k)x2−25x+10</p><p>                       −−4x3−+8x2+−4kx</p><p>                       (8−k)x2+(4k−25)x+10</p><p>                       −(8−k)x2+−(2k−16)x−+(8k−k2)</p><p>                       (2k−9)x+(k2−8k+10)</p><p>But remainder is given x+a</p><p>∴x+a=(2k−9)x+(k2−8k+10)</p><p>On equating coefficient, we get</p><p>2k−9=1⇒k=5</p><p>and a=k2−8k+10⇒a=25−40+10=−5</p><p>Hence, k=5,a=−5</p><p></p><p>$

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