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Mathematics

Solve the following equation using the formula :

3x2 + 2x - 1 = 0

Quadratic Equations

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Answer

Comparing 3x2 + 2x - 1 = 0 with ax2 + bx + c = 0 we get,

a = 3, b = 2, c = -1.

We know that,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get,

⇒x=−(2)±(2)2−4(3)(−1)2(3)=−2±4+126=−2±166=−2±46=−1±23=−1+23 or −1−23=13 or −33=13 or −1.\Rightarrow x = \dfrac{-(2) \pm \sqrt{(2)^2 - 4(3)(-1)}}{2(3)} \\[1em] = \dfrac{-2 \pm \sqrt{4 + 12}}{6} \\[1em] = \dfrac{-2 \pm \sqrt{16}}{6} \\[1em] = \dfrac{-2 \pm 4}{6} \\[1em] = \dfrac{-1 \pm 2}{3} \\[1em] = \dfrac{-1 + 2}{3} \text{ or } \dfrac{-1 - 2}{3} \\[1em] = \dfrac{1}{3} \text{ or } \dfrac{-3}{3} \\[1em] = \dfrac{1}{3} \text{ or } -1.

Hence, x = −1,13-1, \dfrac{1}{3}.

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