Question

is anyone there ple..help me solve this question na ple.. :(((​

Answer 1

Step-by-step explanation:

$\large 3 {x}^{2} + 7x + 2 = 0$

$→ \large 3 {x}^{2} + 6x + x + 2 = 0$

$→ \large 3x(x + 2) + 1(x + 2) = 0$

$→ \large (3x + 1)(x + 2) = 0$

$→ \large x = \frac{ - 1}{3} \: \: \: \: \: \: \: \: ,\: \: \: \: \: \: \: \: x = - 2$

$\large let \: \: \alpha = \frac{ - 1}{3} \: \: and \: \: \beta = - 2$

$\large a = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: b \: = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: c = 2$

Now , according to the first relation ,

$\alpha + \beta = \Large\frac{ - b}{a}$ (sum of coefficients)

$→ \Large \frac{ - 1}{3} + \small( - 2) = \Large\frac{ - 7}{3}$

$→ \Large \frac{ - 1 + 3 \times ( - 2)}{3} = \Large\frac{ - 7}{3}$

$→ \Large \frac{ - 1 + ( - 6)}{3} = \Large\frac{ - 7}{3}$

$→ \Large \frac{ - 1 - 6}{3} = \Large\frac{ - 7}{3}$

$→ \Large \frac{ -7}{3} = \Large\frac{ - 7}{3}$

Now , according to the second relation ,

$\alpha \beta = \Large\frac{c}{a}$ (products of coefficients)

$→\Large\frac{ - 1}{3} \small \times ( - 2) = \Large \frac{2}{3}$

$→\Large\frac{ - 1 \times ( - 2)}{3} = \Large \frac{2}{3}$

$→\Large\frac{ 2}{3} = \Large\frac{2}{3}$

Note -

• $\large( - )( - ) = +$
• $\large( + )( - ) = -$
• $\large( - )( + ) = -$
• $\large( + )( + ) = +$