Grade 99 grade maths
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
1 Answer
Nishant Vora
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
Other Related Questions on 9 grade maths
What are the differences between similar triangles and congruent triangles?
What are the differences between similar triangles and congruent triangles?
9 grade maths
Last Activity: 0 Years ago
The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
- (a) 12
- (b) 4
- (c) 20
- (d) 44
The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
- (a) 12
- (b) 4
- (c) 20
- (d) 44
9 grade maths
Last Activity: 0 Years ago