Question

Find the root of root3x²+10x-8root3=0

Answer 1

Answer:

$\boxed{\underline{\boxed{\bold{x = 3.07, 0.25}}}}$

Step-by-step explanation:

$3x^2 + 10x - 8 \sqrt{3} = 0\\\\\text{A standard quadratic equation is of the form:}\\\\ax^2 + bx + c = 0\\\\\text{On comparing the above two equations, we get:}\\\\a = 3\\\\b = 10\\\\c = -8\sqrt{3}\\\\\text{We know that discriminant, D = b^2 - 4ac }\\\\\implies D = (-8\sqrt{3})^2 - 4(3)(10)\\\\\implies D = 64(3) - 120\\\\= 192 - 120\\\\= 72\\\\\text{Since D is +ve and D > 0,}\\\text{the given quadratic equation has}\\\text{real and unequal roots.}$

$\text{Using the quadratic formula,}\\\text{(For derivation, refer link at the end of this answer.)}\\\\x = \dfrac{-b \pm \sqrt{D}}{2a}\\\\\\= \dfrac{-10 \pm \sqrt{72}}{2(3)}\\\\\\= \dfrac{-10 \pm \sqrt{2 \times 2 \times 2 \times 3 \times 3}}{6}\\\\\\= \dfrac{-10 \pm 6\sqrt{2}}{6}\\\\\\\text{Put \sqrt{2} = 1.41 }\\\\x = \dfrac{-10 \pm 6 \times 1.41}{6}\\\\\\= \dfrac{-10 \pm 8.46}{6}\\\\\\\implies x = \dfrac{-10 - 8.46}{6}, \dfrac{-10 + 8.46}{6}$

$\implies x = \dfrac{-18.46}{6}, \dfrac{-1.54}{6}\\\\\\\implies \boxed{\underline{\boxed{\bold{x = 3.07, 0.25}}}}$

Derivation of quadratic formula: https://brainly.in/question/9260162

Answer 2

Question:-⬇️

Find the root of root3x²+10x-8root3=0

Answer:-⬇️

$\boxed{\underline{\boxed{\bold{x = 3.07, 0.25}}}}$Step-by-step explanation:$3x^2 + 10x - 8 \sqrt{3} = 0\\\\\text{A standard quadratic equation is of the form:}\\\\ax^2 + bx + c = 0\\\\\text{On comparing the above two equations, we get:}\\\\a = 3\\\\b = 10\\\\c = -8\sqrt{3}\\\\\text{We know that discriminant, D = b^2 - 4ac }\\\\\implies D = (-8\sqrt{3})^2 - 4(3)(10)\\\\\implies D = 64(3) - 120\\\\= 192 - 120\\\\= 72\\\\\text{Since D is +ve and D > 0,}\\\text{the given quadratic equation has}\\\text{real and unequal roots.}$$\text{Using the quadratic formula,}\\\text{(For derivation, refer link at the end of this answer.)}\\\\x = \dfrac{-b \pm \sqrt{D}}{2a}\\\\\\= \dfrac{-10 \pm \sqrt{72}}{2(3)}\\\\\\= \dfrac{-10 \pm \sqrt{2 \times 2 \times 2 \times 3 \times 3}}{6}\\\\\\= \dfrac{-10 \pm 6\sqrt{2}}{6}\\\\\\\text{Put \sqrt{2} = 1.41 }\\\\x = \dfrac{-10 \pm 6 \times 1.41}{6}\\\\\\= \dfrac{-10 \pm 8.46}{6}\\\\\\\implies x = \dfrac{-10 - 8.46}{6}, \dfrac{-10 + 8.46}{6}$$\implies x = \dfrac{-18.46}{6}, \dfrac{-1.54}{6}\\\\\\\implies \boxed{\underline{\boxed{\bold{x = 3.07, 0.25}}}}$