Question

find the roots of the quadratic equation 2 X square + 5 x + 3 equal to zero using formula method ​

Answer 1

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Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$


$\underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \bold{A \: \: quadratic \: \: equation \: \: in \: \: the \: \: form \: \: of} \\ \bold{ax {}^{2} + bx + c = 0 \: ,\: then } \\ \\ \bold{x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac } }{2a} }$


$\bold{2x {}^{2} + 5x + 3 = 0}$


$\bold{Here,} \\ \\ \bold{a = 2} \\ \\ \bold{b = 5} \\ \\ \bold{c = 3}$


$\bold{ \therefore \: x = \frac{ - 5 \: \pm \: \sqrt{(5) {}^{2} - 4 \times 2 \times 3 \: } \: \: }{2 \times 2} } \\ \\ \bold{ = \frac{ - 5 \: \pm \: \sqrt{25 - 24 \: \: } }{4} } \\ \\ \bold{ = \frac{ - 5 \: \pm \: \sqrt{1} }{4} } \\ \\ \bold{ = \frac{ - 5 \: \pm \: 1}{4} }$

$\bold{ \therefore \: x = \frac{ - 5 + 1}{4} = \frac{ - 4}{4} = - 1 } \\ \\ \bold{Or,} \\ \\ \bold{ \: \: \: \: \: x = \frac{ - 5 - 1}{4} = \frac{ - 6}{4} = - \: \frac{3}{2} }$

$\bold{ \therefore \: \: The \: \: roots \: \: of \: \: the \: \: quadratic \: \: equation} \\ \bold{2x {}^{2} + 5x + 3 = 0 \: \: are \: \: : \: \: \: - 1 \: \: \: Or, \: \: \: - \: \frac{3}{2} }$