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q - p*x^2 %2B 2*(text*(x^4*(i*(s*(a*(f*(a*(c*(t*(o*(r*(f*o)))))))))))) %2B x^2 - 3*x=0 |
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Answer» Given:x²-3x+2 is a factor of x⁴-px²+q=0 To prove:p=5; q=4 Solution:x²-3x+2=0sum=-3; product=2number=-2,-1x²-2x-x+2=0x(x-2)-1(x-2)=0(x-1)(x-2)=0x=1,2 p(x) =x⁴-px²+qp(1)=1-p+q0=1-p+qp-q=1...(1) p(2)=16-4p+q4p-q=16...(2)solving (1)&(2) -3p=-15p=5substituting p=5in (1) 5-1=qq=4 Thus p=5; q=4 |
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