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Solving a Quadratic Equation by Completion of Squares Method

The number of...

Question

The number of real zeros of the quadratic polynomial $3 x^{2} - x - 4$ are

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Solution

$3 x^{2} - x - 4$
$= 3 x^{2} - 4 x + 3 x - 4$
$= x (3 x - 4) + 1 (3 x - 4)$
$= (3 x - 4) (x + 1)$
$\Rightarrow (3 x - 4) = 0$ or $(x + 1) = 0$
$\Rightarrow x = \frac{4}{3}$ or $x = - 1$
The zeros of the polynomials are $\frac{4}{3}$ , $- 1$

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