# The sum of zeroes of the polynomial f(x) = 2³- 3² + 4x – 5 is 6, then the value of k isa) 2b) -2 December 19, 2021 by Athena

The sum of zeroes of the polynomial f(x) = 2³- 3² + 4x – 5 is 6, then the value of k is

a) 2

b) -2

c) 4

d) -4

### 2 thoughts on “The sum of zeroes of the polynomial f(x) = 2³- 3² + 4x – 5 is 6, then the value of k is<br /><br />a) 2<br /><br />b) -2<br /><br”

Step-by-step explanation:

2. ## QUESTION:

• The sum of zeroes of the polynomial f(x) = 2x³- 3kx² + 4x – 5 is 6, then the value of k is?

### Given:

• f(x) = 2x³- 3kx² + 4x – 5
• Sum of zeroes = 6

• Value of k

### Solution:

$$\text{We are given that,}\\\:\longrightarrow f(x)=2x^3-3kx^2+4x-5\\\\\text{We know that,}\\\\\text{For a cubic polynomial, p(x)=ax^2+bx^2+cx+d,}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{\text{Coefficient of x^2}}{\text{Coefficient of x^3}}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{b}{a}\\\\\text{So,}\\\\\text{Here, a = 2 and b = -3k. So,}\\\\:\implies\text{Sum of zeroes}=-\dfrac{-3k}{2}\\\\:\implies\text{Sum of zeroes}=\dfrac{3k}{2}$$

$$\text{But, we are given that,}\\\\:\longrightarrow\text{Sum of zeroes}=6\\\\\text{So,}\\\\:\implies\dfrac{3k}{2}=6\\\\\text{On cross-multiplying,}\\\\:\implies3k=6\times2\\\\:\implies3k=12\\\\\text{On transposing 3 to RHS,}\\\\:\implies k=\dfrac{12\!\!\!\!\!/^{\:\:4}}{3\!\!\!/}\\\\\bf{:\implies k=4}\\\\\text{\bf{Hence, value of ‘k’ is 4(Option C).}}$$

### Formula Used:

$$\text{For a cubic polynomial, p(x)=ax^2+bx^2+cx+d,}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{\text{Coefficient of x^2}}{\text{Coefficient of x^3}}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{b}{a}$$
{"found_math": true, "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": 1, "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://wiki-helper.com/the-sum-of-zeroes-of-the-polynomial-f-2-3-4-kitu-5-is-6-then-the-value-of-k-is-a-2-b-39825584-63/", "fetch_time": 1713036954000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-18/segments/1712296816832.57/warc/CC-MAIN-20240413180040-20240413210040-00378.warc.gz", "warc_record_offset": 582531772, "warc_record_length": 13484, "token_count": 682, "char_count": 1665, "score": 4.65625, "int_score": 5, "crawl": "CC-MAIN-2024-18", "snapshot_type": "latest", "language": "en", "language_score": 0.5683754682540894, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00010-of-00064.parquet"}