# 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:

$$\text{For a cubic polynomial, p(x)=ax^2+bx^2+cx+d,}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{\text{Coefficient of x^2}}{\text{Coefficient of x^3}}\\\\:\hookrightarrow\text{Sum of zeroes}=-\dfrac{b}{a}$$