If the y-coordinate of the vertex of the graph of $y = {ax}^{2} + bx + c, a < 0$ is zero, then the zero of the quadratic polynomial is equal to

\frac{- b^{2} + 4 ac}{2 a}

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\frac{c}{a}

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- \frac{b}{a}

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- \frac{b}{2 a}

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Solution

The correct option is D $- \frac{b}{2 a}$
Given: $y = {ax}^{2} + bx + c, a < 0$

Vertex of the graph is given by $(\frac{- b}{2 a}, \frac{- D}{4 a}), where D = b^{2} - 4 ac .$

Given that, y-coordinate of vertex is zero.

$∴ \frac{- D}{4 a} = 0$
$\Rightarrow D = 0$

Now, $x = \frac{- b \pm \sqrt{D}}{2 a} = \frac{- b}{2 a} (∵ D = 0)$

Hence, the correct answer is option (d).

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