Respected Sir- Please help me in solving my below mentioned doubt-If x2-1 is a factor of a x4-b x3-c x2-d x-e- then1- a - c - e - b - d2 - a-b-e-c-d3- a - b - c - d - e4- b - c - d - a - e

if x2 1 is a factor of ax4+bx3+cx2+dx+e = gt; 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= ...

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Standard X

Mathematics

Factor Theorem

Respected Sir...

Question

Respected Sir,

Please help me in solving my below mentioned doubt:

If x² - 1 is a factor of ax⁴+ bx³+ cx²+ dx + e, then

1. a+c+e=b+d

2.a+b+e=c+d

3. a+b+c=d+e

4. b+c+d=a+e

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Solution

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 ANSWER IS ONE.

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Similar questions

Q. If x² − 1 is a factor of ax⁴ + bx³ + cx² + 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

Q. If

x^{2} - 1

is a factor of

a x^{4} + b x^{3} + c x^{2} + d x + e

, then prove that
(a)

a + b + c + d + e = 0

(b)

a + c + e = b + d

Q. If

(x^{2} - 1)

is factor of

a x^{4} + b x^{3} + c x^{2} + d x + e

, show that

a + c + e = b + d = 0

Q. State True or False.

x^{2} - 1

is a factor of

a x^{4} + b x^{3} + c x^{2} + d x + e

, then

a + c + e = b + d = 0

Q. If

x^{3} + 1

is a factor of

a x^{2} + b x^{3} + c x^{2} + d x + e,

a, b, c, d, e

ϵ R a n d a \neq 0,

then the real root of

a x^{4} + b x^{3} + c x^{2} + d x + e = 0

other than -1 is

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Respected Sir, Please help me in solving my below mentioned doubt: If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e, then 1. a+c+e=b+d 2.a+b+e=c+d 3. a+b+c=d+e 4. b+c+d=a+e

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 ANSWER IS ONE.

Respected Sir,

Please help me in solving my below mentioned doubt:

If x² - 1 is a factor of ax⁴+ bx³+ cx²+ dx + e, then

1. a+c+e=b+d

2.a+b+e=c+d

3. a+b+c=d+e

4. b+c+d=a+e