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Find the nature of roots of the equation $3x^2 - 4\sqrt{3}x + 4 = 0$.
Find the nature of roots of the equation $3x^2 - 4\sqrt{3}x + 4 = 0$.
This Question has 1 answers.
We are given the quadratic equation:
$ \displaystyle 3x^2 - 4\sqrt{3}x + 4 = 0 $
### Step 1: Calculate the Discriminant
The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0$ is given by:
$ \displaystyle \Delta = b^2 - 4ac $
Substituting $a = 3$, $b = -4\sqrt{3}$, and $c = 4$:
$ \displaystyle \Delta = (-4\sqrt{3})^2 - 4(3)(4) $
$ \displaystyle = 48 - 48 = 0 $
### Step 2: Determine the Nature of Roots
Since the discriminant $\Delta = 0$, the quadratic equation has real and equal roots.
$ \displaystyle 3x^2 - 4\sqrt{3}x + 4 = 0 $
### Step 1: Calculate the Discriminant
The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0$ is given by:
$ \displaystyle \Delta = b^2 - 4ac $
Substituting $a = 3$, $b = -4\sqrt{3}$, and $c = 4$:
$ \displaystyle \Delta = (-4\sqrt{3})^2 - 4(3)(4) $
$ \displaystyle = 48 - 48 = 0 $
### Step 2: Determine the Nature of Roots
Since the discriminant $\Delta = 0$, the quadratic equation has real and equal roots.
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