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Solve the equation $4x^2 - 9x + 3 = 0$, using quadratic formula
Solve the equation $4x^2 - 9x + 3 = 0$, using quadratic formula
This Question has 1 answers.
We are given the quadratic equation:
$ \displaystyle 4x^2 - 9x + 3 = 0 $
### Step 1: Identify Coefficients
Comparing with the standard quadratic equation $ax^2 + bx + c = 0$:
$ a = 4, \quad b = -9, \quad c = 3 $
### Step 2: Apply the Quadratic Formula
The quadratic formula is:
$ \displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $
Substituting the values of $a$, $b$, and $c$:
$ \displaystyle x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(4)(3)}}{2(4)} $
$ \displaystyle = \frac{9 \pm \sqrt{81 - 48}}{8} $
$ \displaystyle = \frac{9 \pm \sqrt{33}}{8} $
### Final Answer: $ \displaystyle x = \frac{9 + \sqrt{33}}{8}, \quad x = \frac{9 - \sqrt{33}}{8} $
$ \displaystyle 4x^2 - 9x + 3 = 0 $
### Step 1: Identify Coefficients
Comparing with the standard quadratic equation $ax^2 + bx + c = 0$:
$ a = 4, \quad b = -9, \quad c = 3 $
### Step 2: Apply the Quadratic Formula
The quadratic formula is:
$ \displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $
Substituting the values of $a$, $b$, and $c$:
$ \displaystyle x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(4)(3)}}{2(4)} $
$ \displaystyle = \frac{9 \pm \sqrt{81 - 48}}{8} $
$ \displaystyle = \frac{9 \pm \sqrt{33}}{8} $
### Final Answer: $ \displaystyle x = \frac{9 + \sqrt{33}}{8}, \quad x = \frac{9 - \sqrt{33}}{8} $
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