Question

find the roots of the following quadratic
equation
2x^2/5 -x-3/5= 0​

Answer 1

$\red{\underline{\underline{Answer:}}}$

$\sf{Roots \ are \ 3 \ and \ \frac{-1}{2}}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{\frac{2x^{2}}{5}-x-\frac{3}{5}=0}}$

$\sf\pink{To \ find:}$

$\sf{Roots \ of \ the \ equation.}$

$\sf{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{\frac{2x^{2}}{5}-x-\frac{3}{5}=0}}$

$\sf{Multiply \ equation \ throughout \ by \ 5}$

$\sf{\implies{2x^{2}-5x-3=0}}$

$\sf{\implies{2x^{2}-6x+x-3=0}}$

$\sf{\implies{2x(x-3)+1(x-3)}}$

$\sf{\implies{(x-3)(2x+1)=0}}$

$\sf{\implies{\therefore{x=3 \ or \ \frac{-1}{2}}}}$

$\sf\purple{\tt{\therefore{Roots \ are \ 3 \ and \ \frac{-1}{2}}}}$

Answer 2

$\huge\underline\mathfrak\red{Question:}$

$\rm{Find \ the \ roots \ of \ following \ quadratic \ equation}$

$\frac{2 {x}^{2}}{5} - x - \frac{3}{5} =0$

_________________________________________

$\huge\underline\mathfrak\blue{Answer:}$

$\rm\orange{ the \ roots \ of \ the \ quadratic \ equation \ are }$

$\rm\orange{- \frac{1}{2} \ and \ 3 }$

_________________________________________

$\sf\large\underline\green{Given: }$

$\rm{Given \ quadratic \ equation \ is :}$

$\frac{2 {x}^{2}}{5} - x - \frac{3}{5} =0$

_________________________________________

$\sf\large\underline\green{To \ find : }$

$\rm{Roots \ of \ the \ quadratic \ equation}$

_________________________________________

$\huge\underline\mathfrak\orange{Solution:}$

$\rm{Given \ quadratic \ equation \ is :}$

$\frac{2 {x}^{2}}{5} - x - \frac{3}{5} =0$

$\rm{multiplying \ both \ sides \ by \ 5}$

$\rm{we \ get ,}$

$2 {x}^{2} - 5 - 3 = 0$

$\rm{now , \ we've \ to \ split \ middle \ term}$

$\rm{such \ that \ addition \ is \ -5 \ and \ product \ is \ -6 :}$

$\rm{so , \ we \ have \ to \ take \ -6 \ and \ 1}$

$2 {x}^{2} - 6x + x - 3$

$2x( x- 3) + 1(x - 3) = 0$

$(2x + 1)(x - 3) = 0$

$2x + 1 = 0 \: \: and \: \: \: x - 3 = 0$

$x = - \frac{1}{2}$

$and$

$x = 3$

$\rm\orange{hence, \ the \ roots \ of \ the \ quadratic \ equation \ are }$

$\rm\orange{- \frac{1}{2} \ and \ 3 }$

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$\rm\red{ hope \ it \ helps }$ :))