if x2-1 is a factor of ax4+bx3+cx2+dx+e, show that a+c+e=b+d=0
if x2-1 is a factor of ax4+bx3+cx2+dx+e, show that a+c+e=b+d=0
Asiya Hassan , 11 Years ago
Grade 9
9 grade maths> if x2-1 is a factor of ax4+bx3+cx2+dx+e, ...
1 Answers
Nishant Vora
Last Activity: 11 Years ago
Hello student, Please find the soluiton
if x2-1 is a factor of ax4+bx3+cx2+dx+e
=> x = +1 and -1 are the roots of ax4+bx3+cx2+dx+e
Now if f(x) = ax4+bx3+cx2+dx+e
than f(+1)=f(-1)=0
so 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
I hope the solution is clear
Thank you
if x2-1 is a factor of ax4+bx3+cx2+dx+e
=> x = +1 and -1 are the roots of ax4+bx3+cx2+dx+e
Now if f(x) = ax4+bx3+cx2+dx+e
than f(+1)=f(-1)=0
so 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
I hope the solution is clear
Thank you
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