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find k so that xsquare +2x +k is a factor of    2x to the power 4 +xcube -14x square +5x +6  also find all the zeroes of the two polynomials
Asked by ajayrath7 | 07 Apr, 2019, 07:19: PM

2x2 -3x -(8+2k)
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x2 +2x +k ) 2x4 +x3 -14x2 +5x +6
2x4 +4x3 +2k x2
----------------------
-3x3 -(14+2k) x2 +5x
-3x3 -6 x2 -3kx
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-(8+2k)x2 + (5+3k)x +6
-(8+2k)x2 - (16+4k)x -(8+2k)k
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(21+7k)x +(2k2 +8k+6)

if ( x2 +2x +k ) is exact divisior, then  (21+7k)x +(2k2 +8k+6) = 0   ..................(1)

Eqn.(1) is true if   21+7k = 0   and  (2k2 +8k+6) = 0 . This is valid if k = -3

Hence x2 +2x +k = x2 +2x -3 = (x+3)(x-1)  or zeroes of this polynoimal are -3 and 1

2x4 +x3 -14x2 +5x +6 = ( x2 +2x -3 ) ( 2x2 -3x -2 ) = (x+3)(x-1)(2x+1)(x-2)  or zeroes of this polynomial are -3, 1, -1/2 and 2
Answered by Thiyagarajan K | 08 Apr, 2019, 07:05: AM

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