Question

If the product of the zeroes of the quadratic polynomial x 2 - 4x + k is 3 then, find the value of k. Also find the sum of the zeroes of the polynomial?​

Answer 1

Answer:

Step-by-step explanation:

product of zeroes= c/a= k/1=3

k=3

x^2-4x+3

this equation has roots 1,3

Answer 2

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given Polynomial:

$\sf = {x}^{2} - 4x + k$

Comparing it with ax² + bx + c, we get:

$\begin{cases} \sf a = 1 \\ \sf b = - 4 \\ \sf c = k\end{cases}$

We know that:

$\sf \implies Product \: Of \: Zeros = \dfrac{c}{a}$

Therefore, as per the data provided:

$\sf \implies 3 = \dfrac{k}{1}$

$\sf \implies k = 3$

So, the quadratic polynomial is:

$\sf = {x}^{2} - 4x + 3$

Also, we know that:

$\sf \implies Sum \: Of \: Zeros = \dfrac{ - b}{a}$

$\sf = \dfrac{ - ( - 4)}{1}$

$\sf =4$

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• The value of k is 3.
• The sum of the zeros of the polynomial is 4.