What are the zeros of the polynomial x2-6x+k. What is the value of k o

1.	What are the zeros of the polynomial x2-6x+k. What is the value of k of 3alpha+2beta=20.
Answer» AnsWer : k = -16. Given : We have expression x² -6X + k. 3 alpha + 2beta = 20. To Find : Value of k. Concepts Required : $\tt \blacksquare \: <klux>SUM</klux> \: of \: Zeros. \\ \tt \alpha + \beta = \frac{ - b}{a}$ $\tt \blacksquare \: Product \: of \: Zeros. \\ \tt \alpha . \beta = \frac{ c}{a}$ SOLUTION : We have, $\tt \: \: 3 \alpha + <klux>2</klux> \beta = 20. - - - (<klux>1</klux>)$ Sum of zeros, $\tt \: \: \alpha + \beta = \frac{ - b}{a} = 6 - - - (2)$ And, Product of zeros, $\tt \: \: \alpha . \beta = \frac{c}{a} = k - - - (3)$ $\rule{200}3$ Now, Taking equation (2) $\tt \implies \alpha + \beta = 6$ Multiply by 2, We get. $\tt \implies2 \alpha +2 \beta = 12. - - -( 4)$ By equation 1 Subtracted From equation 4, We get. $\begin{tabular}{1-1} 3 \alpha + 2 \beta= 20 & \\ 2 \alpha +2 \beta = 12 & \\ \cline{1-1} \alpha = 8 & \\ \cline{1-1} \end{tabular}$ $\tt \implies \alpha = 8.$ Putting the value of alpha in equation 2. $\tt \implies\alpha + \beta = 6.$ $\tt \implies8 + \beta = 6.$ $\tt \implies \beta = - 2.$ $\rule{200}3$ Now, According to Question. Putting the value of alpha and beta in equation 3, We get the value of k. $\tt \implies \alpha \beta = k$ $\tt \implies8 \times - 2 = k.$ $\tt \implies k = - 16.$ Therefore,the value of k is -16.