Find the roots of the quadratic equation 62 − − 2 = 0.

We have been given the quadratic equation 6𝑥 and we need to find 6𝑥2 − 𝑥 − 2 = 0 its roots.6𝑥2 − 𝑥 − 2 = 0Factorising by splitting the middle term, we get⇒6𝑥2 + 3𝑥 − 4𝑥 − 2 = 0Taking terms common,⇒3x(2x+1)−2(2x+1)=0⇒(2x+1)(3x−2)=0⇒2x+1=0 or (3x−2)=0⇒x=−12 or 23

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Find the roots of the quadratic equation 6𝑥² − 𝑥 − 2 = 0.

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Detailed Solution

We have been given the quadratic equation 6𝑥 and we need to find 6𝑥² − 𝑥 − 2 = 0 its roots.

6𝑥² − 𝑥 − 2 = 0

Factorising by splitting the middle term, we get

⇒6𝑥² + 3𝑥 − 4𝑥 − 2 = 0

Taking terms common,

$\begin{aligned} \Rightarrow 3 x (2 x + 1) - 2 (2 x + 1) = 0 \\ \Rightarrow (2 x + 1) (3 x - 2) = 0 \\ \Rightarrow 2 x + 1 = 0 or \\ (3 x - 2) = 0 \\ \Rightarrow x = \frac{- 1}{2} or \frac{2}{3} \end{aligned}$