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Quadratic Formu.

Solve the following equa
(a)
2x^(2)+x-3=0

Quadratic Formu. $\newline$ $1$ . Solve the following equa $\newline$ (a) $2 x^{2}+x-3=0$

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Quadratic equation with complex roots

Full solution

Q. Quadratic Formu.

\newline

1

. Solve the following equa

\newline

(a)

2 x^{2}+x-3=0

Identify coefficients: Identify coefficients $a$ , $b$ , and $c$ in the quadratic equation $2x^2 + x - 3 = 0$ . $\newline$ $a = 2$ , $b = 1$ , $c = -3$ .
Use quadratic formula: Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Substitute $a = 2$ , $b = 1$ , $c = -3$ into the formula.
Calculate discriminant: Calculate the discriminant $b^2 - 4ac$ . $\newline$ Discriminant = $1^2 - 4(2)(-3) = 1 + 24 = 25$ .
Calculate square root: Calculate the square root of the discriminant $\sqrt{25}$ . $\newline$ Square root = $\sqrt{25} = 5$ .
Substitute discriminant: Substitute the discriminant into the quadratic formula. $\newline$ $x = \frac{{-1 \pm \sqrt{5}}}{{2 \cdot 2}}$ .
Simplify expression: Simplify the expression to find the two roots. $\newline$ $x = \frac{{-1 + 5}}{{4}}$ and $x = \frac{{-1 - 5}}{{4}}$ . $\newline$ $x = \frac{{4}}{{4}}$ and $x = \frac{{-6}}{{4}}$ . $\newline$ $x = 1$ and $x = -1.5$ .

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