Maharashtra BoardEnglish MediumSTD 10MathsP-1 Quadratic Equations3 Marks
Question
Solve the following quadratic equation by completing the square method. 2y2 + 9y + 10 = 0
✓
Answer
$2 y^2+9 y+10=0$ Steps involved in solving quadratic equation by completing the square method are - 1. Making the first variable free of coefficient Dividing by the coefficient of 2 , we get, $\Rightarrow y^2+\frac{9}{2} y+5=0$ 2. The coefficient of linear variable(variable with degree 1 ) is then squared and then added and subtracted from the equation. $\Rightarrow y ^2+\frac{9}{2} y +\frac{81}{16}-\frac{81}{16}+5=0$ 3. Take out the terms following the formula $(a+b)^2=a^2+b^2+2 a b$ $\Rightarrow\left(y^2+\frac{9}{2} y+\frac{81}{16}\right)-\left(\frac{81}{16}-5\right)=0$ $\begin{array}{l}\Rightarrow y+\frac{9}{2}=\frac{1}{4} \text { or } y+\frac{9}{2}=-\frac{1}{4} \\ \Rightarrow y=\frac{1}{4}-\frac{9}{2} \text { or } y=-\frac{1}{4}-\frac{9}{2} \\ \Rightarrow y=\frac{1-18}{4} \text { or } y=\frac{-1-18}{4} \\ \Rightarrow y=-\frac{17}{4} \text { or } y=-\frac{19}{4}\end{array}$
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