Question

find the value of a in equation 3x^2-(3a+2)x+7=0 if one of its root is 4?​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \: - \begin{cases} &\sf{a \: quadratic \: {3x}^{2} - (3a + 2)x + 7 = 0} \\ &\sf{having \: one \: root \: 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: find \: - \begin{cases} &\sf{value \: of \: a} \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given

• A quadratic equation

$\rm \: \rightarrow \: {3x}^{2} - (3a + 2)x + 7 = 0$

Since,

$\bigstar \: \: \red{ \rm \: According \: to \: statement }$

• 4 is the root of the quadratic equation.

$\rm \: \rightarrow \: 3{(4)}^{2} - (3a + 2) \times 4 \: + 7 = 0$

$\rm \: \rightarrow \: 48 - 12a - 8 + 7 = 0$

$\rm \: \rightarrow \: 47 - 12a = 0$

$\rm \: \rightarrow \: 12a = 47$

$\large \boxed{ \pink{ \rm \: \rightarrow \: a \: = \: \dfrac{47}{12} \: \: }}$