Question
Solve the following quadratic equation by factorization.
$2y^2 + 27y + 13 = 0$
$2y^2 + 27y + 13 = 0$
✓
Answer
$2 y^2+27 y+13=0 $
$\Rightarrow 2 y^2+26 y+y+13=0 $
$\Rightarrow 2 y(y+13)+(y+13)=0 $
$\Rightarrow(2 y+1)(y+13)=0 $
$2 y+1=0 \Rightarrow 2 y=-1 \Rightarrow y=-\frac{1}{2} $
$y+13=0 \Rightarrow y=-13$
Hence, $y =-13$ and $y =-\frac{1}{2}$ are roots of the equation.
$\Rightarrow 2 y^2+26 y+y+13=0 $
$\Rightarrow 2 y(y+13)+(y+13)=0 $
$\Rightarrow(2 y+1)(y+13)=0 $
$2 y+1=0 \Rightarrow 2 y=-1 \Rightarrow y=-\frac{1}{2} $
$y+13=0 \Rightarrow y=-13$
Hence, $y =-13$ and $y =-\frac{1}{2}$ are roots of the equation.
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