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IF x^2-1 is a factor of ax^4+bx^3-cx^2+dx+e=0.Show that a+c+e=b+d=0 |
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Answer» if x²-1 is a factor of ax⁴+bx³+cx²+dx+e=>x = +1 and -1 are the rootsof ax⁴+bx³+cx²+dx+e Now if f(x) = ax⁴+bx³+cx²+dx+ethan f(+1)=f(-1)=0so a+b+c+d+e=0 ….….….(1)and a-b+c-d+e = 0 ….…....(2) Hence from (1) and (2),a+c+e=b+d=0 |
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