Question

Solve the quadratic equation 3x^+11x+10=0 by quadratic formula

Answer 1

Quadratic equation -

→ $\sf{\implies 3 {x}^{2} + 11x + 10 = 0 }$

Quadratic formula -

$\boxed{\sf{ \implies \: \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

Here , a = 3 ; b = 11 ; c = 10

Using the above mentioned formula :-

$\sf{ \implies \: \frac{ - 11 \pm \sqrt{( {11)}^{2} - 4(3)(10) } }{2(3)} }$

$\sf{ \implies \frac{ - 11 \pm \sqrt{121 - 4(30)} }{6} }$

$\sf{ \implies \frac{ - 11 \pm \sqrt{121 - 120} }{6} }$

$\sf{ \implies \frac{ - 11 \pm \sqrt{1} }{6} }$

$\sf{ \implies \frac{ - 11 \pm 1 }{6} }$

Taking positive value :-

$\sf{ \implies \frac{ - 11 + 1 }{6} }$

$\sf{ \implies \frac{ - 10 }{6} }$

$\sf{ \implies \: x \: = \frac{ \cancel{ - 10}}{ \cancel{6}} = \frac{ - 5}{3} }$

Taking negative value :-

$\sf{ \implies \frac{ - 11 -1 }{6} }$

$\sf{ \implies \frac{ - 12 }{6} }$

$\sf{ \implies \: x = -2 }$

$\boxed{ \sf{ \red{ \implies \: x \: = - \frac{5}{3} \: or \: - 2}}}$

Answer 2

$\bf\blue{\boxed{Question}}$

$\:$

$\small\tt{Solve\:the\:quadratic\: equation\:}\\{\small\tt{3x^2+11x+10=0\:\:by\:quad \:formula.}}$

$\:$

$\bf\blue{\boxed{Solution}}$

$\:$

$\rm{\ 3x^{2}-11x+10\:=\:0}$

$\:$

$\rm\red{\boxed{x\:=\:\frac{-b±\sqrt{ \ b^{2}-4ac}}{2a}}}$

$\:$

$\rm{x\:=\:\frac{-11±\sqrt{ \ (11)^{2}-4(3)(10)}}{2\times 3}}$

$\:$

$\rm{x\:=\:\frac{-11±\sqrt{ 121-120}}{6}}$

$\:$

$\rm{x\:=\:\frac{-11±\sqrt{1}}{6}}$

$\:$

$\rm{x\:=\:\frac{-11±1}{6}}$

$\:$

$\small\rm{So\: there\:are\:two\:possible\:values.}$

$\:$

$\small\rm\blue{\underline{\boxed{1.)\:\:\:\: Positive}}}$

$\:$

$\rm{x\:=\:\frac{-11+1}{6}}$

$\:$

$\rm\red{\underline{\boxed{x\:=\:{\cancel\frac{-10}{\:\:\:6}}\:=\: {\frac{-5}{\:\:3}}}}}$

$\:$

$\small\rm\blue{\underline{\boxed{1.)\:\:\:\: Negative}}}$

$\:$

$\rm{x\:=\:\frac{-11-1}{6}}$

$\:$

$\rm\red{\underline{\boxed{x\:=\:\frac{-12}{\:\:\:\:6}\:=\: -2}}}$

$\:$

$\bf\blue{\boxed{Hope\:It\: Help\:You}}$