Question

solve 3x2-2x-3=0 by using quadratic formula​

Answer 1

Hey There,

See The Attachment,

Hope It Helps You

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Answer 2

Given,

Equation,

3x² - 2x - 3 = 0

To find,

Solution using the quadratic formula.

Solution,

Using the quadratic formula, the solution to a given quadratic equation or roots of the equation can be found. Suppose the quadratic equation is,

ax² + bx + c = 0,

Then its solution or roots will be given by the formula,

$x_{1,2}=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}$

Here, the given equation is,

3x² - 2x - 3 = 0

So,

a = 3,

b = -2, and,

c = -3.

Substituting these values in the above formula,

$x_{1,2}=\frac{-(-2)\pm \sqrt{(-2)^{2} -4(3)(-3)} }{2(3)}$

⇒ $x_{1,2}=\frac{2\pm \sqrt{(4) +36} }{6}$

⇒ $x_{1,2}=\frac{2\pm \sqrt{40} }{6}$

⇒ $x_{1,2}=\frac{2\pm 2\sqrt{10} }{6}$

⇒ $x_{1,2}=\frac{1\pm \sqrt{10} }{3}$

⇒ $x_{1}=\frac{1 + \sqrt{10} }{3},x_{2}=\frac{1 - \sqrt{10} }{3},$

Therefore, the solution of the given equations using quadratic formula will be $x_{1}=\frac{1 + \sqrt{10} }{3},x_{2}=\frac{1 - \sqrt{10} }{3}.$