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In the equation \(x^2 + 5x + k = 0, k\) is a constant and

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Source: — Data Sufficiency |
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by deloitte247 » Sat Oct 26, 2019 6:19 pm
Question: what is the value of k?
Statement 1:
$$2\ is\ a\ root\ of\ x^2+5x+k=0$$
With 2 as a root of this quadratic, equation variable x=2.
$$Therefore,\ x^2+5x+k=0$$
$$2^2+5\left(2\right)+k=0$$
$$14+k=0$$
$$constant\ k=-14$$

Statement 1 is SUFFICIENT

Statement 2:
$$\left(x+7\right)\ is\ a\ factor\ of\ x^2+5x+k=0$$
$$With\ \left(x+7\right)\ as\ a\ factor\ of\ this\ quadratic\ equation,\ then\ x+7=0$$
x=-7
$$Therefore,\ x^2+5x+k=0$$
$$Therefore,\ -7^2+5\left(-7\right)+k=0$$ \
$$49-35+k=0$$
k=-14
Statement 2 is also SUFFICIENT.

In conclusion, each statement alone is SUFFICIENT. Hence, the correct answer is option D.

Thanks
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