How do you solve $2 x^{2} + 5 x - 3 = 0$ ?

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Solution

Compute the roots.
Given : $2 x^{2} + 5 x + 3 = 0$
Since, $2 x^{2} + 5 x + 3 = 0$ is a quadratic equation, we will use the method of splitting the middle term.
$2 x^{2} + 5 x + 3 = 0$
$\Rightarrow 2 x^{2} + 3 x + 2 x + 3 = 0$ [ splitting the middle term ]
$\Rightarrow x (2 x + 3) + 1 (2 x + 3) = 0$ [ taking $x$ common from $1^{s t}$ and $2^{n d}$ term and $1$ from $3^{r d}$ and $4^{t h}$ term ]
$\Rightarrow (2 x + 3) (x + 1) = 0$ [ $(2 x + 3)$ common ]
From the above equation,
$(2 x + 3) = 0 \Rightarrow x = - \frac{3}{2}$
$(x + 1) = 0 \Rightarrow x = - 1$
Hence, $x = - 1, x = - \frac{3}{2}$ are solution of the equation $2 x^{2} + 5 x + 3 = 0$ .

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