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Verified answer

Answer:

Now we factorise this equation-----

[tex]\begin{gathered}3 {x}^{2} - 4x + 3x - 4 = 0 \\ \\ x(3x - 4) + 1(3x - 4) = 0 \\ \\ (3x - 4)(x + 1) = 0 \\ \\ 3x - 4 = 0 \: \: \: \: \bold{or} \: \: x + 1 = 0 \\ \\ \bold{x = \frac{4}{3} \: \: \: or \: \: \: x = - 1}\end{gathered} \\ \begin{gathered} \\ \\ \: \bold{ \alpha = \frac{4}{ 3} \: \: \: \: or \: \: \: \beta = - 1} \\ \\ \end{gathered} \\ \begin{gathered}equation = 3 {x}^{2} - x - 4 \\ \\ here..... \\ a = 3 \: \\ b = - 1 \\ c = - 4\end{gathered} [/tex]

Now , Verification of Zeroes of polynomial and Coefficient of polynomial.

[tex]\huge{ \bold{ \underline{ \pink{ \: STEP - I }}}} \\ \begin{gathered} \bold{ \alpha + \beta = \frac{ - b}{a} } \\ \\ \frac{4}{3} +( - 1) = \frac{ - ( - 1)}{3} \\ \\ \frac{4}{3} - 1 = \frac{1}{3} \\ \\ \frac{4 - 3}{3} = \frac{1}{3} \\ \\ \frac{1}{3} = \frac{1}{3} \end{gathered} [/tex]

[tex]\huge{ \underline{ \bold{ \pink{ \: \: STEP-II \: \: \: }}}} \\ {\bold{ \alpha \times \beta = \frac{c}{a} }}

\begin{gathered} \\ \frac{4}{3} \times - 1 = \frac{ - 4}{3} \\ \\ \frac{ - 4}{3} = \frac{ - 4}{3} \end{gathered} [/tex]

Here , LHS = RHS

[tex]\huge{ \underline{ \bold{ \red{ \: \: \: \: \: Hence, Verified \: \: \: \: \: \: }}}} [/tex]