Q. 55.0( 3 Votes )

# Prove that if x<s

Given, ax3 + bx2 + cx + d

Need to show a = – c and b = – d if x2 – 1 is a factor

consider, x2 – 1 is a factor of ax3 + bx2 + cx + d

then x = + 1, x = – 1

substitute x value in the equation ax3 + bx2 + cx + d

We get as follows

for x = 1 we get a(1)3 + b(1)2 + c(1) + d

= a + b + c + d ……..eq(1)

for x = – 1 we get a(– 1)3 + b(– 1)2 + c(– 1) + d

= – a + b – c + d ………eq(2)

Solving the two equations we get

(a + b + c + d) + (– a + b – c + d) = 0

b + d = 0

b = – d

And if (a + b + c + d) – (– a + b – c + d) = 0

a + c = 0

a = – c

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

What first degreeKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

In each pair of pKerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2

For each pair of Kerala Board Mathematics Part-2
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://goprep.co/q5-prove-that-if-x-2-1-is-a-factor-of-ax-3-bx-3-cx-d-then-a-i-1nkjr5", "fetch_time": 1624457942000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2021-25/segments/1623488539480.67/warc/CC-MAIN-20210623134306-20210623164306-00432.warc.gz", "warc_record_offset": 267666321, "warc_record_length": 23019, "token_count": 482, "char_count": 1466, "score": 3.703125, "int_score": 4, "crawl": "CC-MAIN-2021-25", "snapshot_type": "latest", "language": "en", "language_score": 0.7950900793075562, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00003-of-00064.parquet"}