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Find the values of $x$ . $\newline$ $3x^2+ 4x+6=0$

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Factor quadratics

Full solution

Q. Find the values of

x

.

\newline

3x^2+ 4x+6=0

Identify Form: Identify the form of the quadratic equation. $\newline$ Equation given is $3x^2 + 4x + 6 = 0$ , which is in standard form $ax^2 + bx + c = 0$ . $\newline$ Here, $a = 3$ , $b = 4$ , and $c = 6$ .
Calculate Discriminant: Calculate the discriminant to check if factoring is possible. $\newline$ Discriminant, $\Delta = b^2 - 4ac = (4)^2 - 4\cdot3\cdot6 = 16 - 72 = -56$ . $\newline$ Since $\Delta$ is negative, the quadratic equation does not have real roots and cannot be factored over the real numbers.

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