Given,
3 x 2 + 10 x + 7 3 = 0 ⇒ 3 x 2 + 7 x + 3 x + 7 3 = 0 ⇒ x ( 3 x + 7 ) + 3 ( 3 x + 7 ) = 0 ⇒ ( x + 3 ) ( 3 x + 7 ) = 0 (Factorising left side) ⇒ x + 3 = 0 or 3 x + 7 = 0 (Zero- product rule) ⇒ x = − 3 or 3 x + 7 = 0 ⇒ x = − 3 or 3 x = − 7 ⇒ x = − 3 or x = − 7 3 x = − 3 or x = − 7 3 3 \sqrt{3}x^2 + 10x + 7\sqrt{3} = 0 \\[1em] \Rightarrow \sqrt{3}x^2 + 7x + 3x + 7\sqrt{3} = 0 \\[1em] \Rightarrow x(\sqrt{3}x + 7) + \sqrt{3}(\sqrt{3}x + 7) = 0 \\[1em] \Rightarrow (x + \sqrt{3})(\sqrt{3}x + 7) = 0 \text{ (Factorising left side) } \\[1em] \Rightarrow x + \sqrt{3} = 0 \text{ or } \sqrt{3}x + 7 = 0 \text{ (Zero- product rule) } \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } \sqrt{3}x + 7 = 0 \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } \sqrt{3}x = -7 \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } x = -\dfrac{7}{\sqrt{3}} \\[1em] x = -\sqrt{3} \text{ or } x = -\dfrac{7\sqrt{3}}{3} 3 x 2 + 1 0 x + 7 3 = 0 ⇒ 3 x 2 + 7 x + 3 x + 7 3 = 0 ⇒ x ( 3 x + 7 ) + 3 ( 3 x + 7 ) = 0 ⇒ ( x + 3 ) ( 3 x + 7 ) = 0 (Factorising left side) ⇒ x + 3 = 0 or 3 x + 7 = 0 (Zero- product rule) ⇒ x = − 3 or 3 x + 7 = 0 ⇒ x = − 3 or 3 x = − 7 ⇒ x = − 3 or x = − 3 7 x = − 3 or x = − 3 7 3
Hence, the roots of given equation are − 3 , − 7 3 3 -\sqrt{3}, -\dfrac{7\sqrt{3}}{3} − 3 , − 3 7 3
