Question

find the zeroes of polynomial 3x2+5x-2 and verify the relationship between zeroes and coefficients????​

Answer 1

⠀⠀⠀⠀$\huge\underline{ \underline{ \bf{ \blue{ \: solution \: : = }}}} </p><p>$

$3 {x}^{2} + 5x - 2$

$3 {x}^{2} + 6x - x - 2 \\ 3x(x + 2) - 1(x + 2) \\ (3x - 1)(x + 2)$

_____________________

⠀$\bf \alpha = \frac{1}{3} \\ \\\bf \beta = - 2$

⠀⠀⠀⠀⠀⠀$\boxed{\pink{\fbox{ \alpha + \beta = \frac{ - b}{a} } }}$

⠀⠀$\frac{1}{3} + ( - 2) = \frac{ - 5}{3} \\ \\ \frac{1 - 6}{3} = \frac{ - 5}{3}$

⠀⠀$\boxed{ \bf{ \frac{ - 5}{3} = \frac{ - 5}{3} }}$

⠀⠀⠀⠀⠀⠀⠀${ \boxed{ \fbox{\red{ \alpha \beta = \frac{c}{a} }}}}$

⠀$\bf \frac{1}{3} \times - 2 = \frac{ - 2}{3}$

⠀⠀⠀⠀⠀⠀⠀⠀${ \boxed{ \bf{ \frac{ - 2}{3} = \frac{ - 2}{3} }}}$

⠀⠀⠀⠀⠀⠀⠀⠀hence verified