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Question -

If x2┬атАУ 1is a factor of ax4┬а+ bx3┬а+ cx2┬а+dx + e, then
(a) a + c + e- b + d
(b
)a + b + e = c + d
(c)a + b + c = d+ e
(d
)b + c + d= a + e



Answer -

X2┬атАУ 1 is a factor of ax4┬а+ bx3┬а+cx2┬а+ dx + e
тЗТ┬а(x + 1), (x тАУ 1) are the factors of ax4┬а+ bx3┬а+cx2┬а+ dx + e
Let f(x) = ax4┬а+ bx3┬а+ cx2┬а+ dx+ e
and x + 1 = 0 then x = -1
тИ┤┬аf(-1) = a(-1)4┬а+ b(-1)3┬а+ c(-1)2┬а+d(-1) + e
= a- b + c- d+ e
тИ┤ x + 1is a factor of f(x)
тИ┤┬аa-b + c- d+e = 0
тЗТ a + c+ e = b + d┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а┬а┬а(a)

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