Question

Find the zeroes of the polynomial 3x 2 – 2x – 8 and verify the relationship between the zeroes and its coefficients​

Answer 1

$\red{\bf {GIVEN :–}}$

• A quadratic equation 3x² - 2x - 8 = 0.

$\red{\bf {TO\: FIND :–}}$

• zeroes of the polynomial = ?

• Verify the relationship between the zeroes and its coefficients.

$\red{\bf {SOLUTION :–}}$

$\begin{gathered} \\ \sf \implies \: \: 3 {x}^{2} - 2x - 8 = 0 \\ \end{gathered}$

$\red{\bf {• Splitting\: Middle\: term –}}$

$\begin{gathered} \\ \sf \implies \: \: 3 {x}^{2} - 6x + 4x - 8 = 0 \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: \: 3x(x - 2) + 4(x - 2)= 0 \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: \: (3x + 4)(x - 2) = 0 \\ \end{gathered}$

$\begin{gathered} \\ \implies \large { \boxed{ \sf x = - \dfrac{4}{3} \:, \: 2}} \\ \end{gathered}$

$\red{\bf {VERIFICATION :–}}$

$\begin{gathered} \\ \sf \longrightarrow \: sum \: \: of \: \: roots \: = \dfrac{ -(coffieciant \: \: of \: \: x)}{coffieciant \: \: of \: \: {x}^{2} } \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: - \dfrac{4}{3} + 2 = \dfrac{ -( - 2)}{3} \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: \dfrac{6 - 4}{3} = \dfrac{2}{3} \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: \dfrac{2}{3} = \dfrac{2}{3} \: \: (verified)\\ \end{gathered}$

$\begin{gathered} \\ \sf \longrightarrow \: product \: \: of \: \: roots \: = \dfrac{constant \: \: term}{coffieciant \: \: of \: \: {x}^{2} } \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: - \dfrac{4}{3} ( 2 ) = \dfrac{ - 8}{3} \\ \end{gathered}$

$\begin{gathered} \\ \sf \implies \: - \dfrac{8}{3} = - \dfrac{8}{3} \: \: (verified)\\ \end{gathered}$

Answer 2

Step-by-step explanation:

very easy step

if u do this u can get full marks

all the best

bye