If k is an integer then x2 7x minus 14 k2 minus 7 8 0 has ........

Quantitative Aptitude (CDS) Quadratic Equations

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If k is an integer, then x²+7x−14(k²−7/8)=0 has

Both integral roots

At least one integral root

No integral root

Both positive integral roots

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Explanation:

we are given that x²+7x−14 (k²−78)=0 let us check the nature of the roots, we have $D=b^{2}-4ac=7^{2}-4\times1\times\14(k^{2}-7/8)$
= 49+56k²− 49=56
Now,
$x= \frac{{}-b\pm \sqrt{D}}{2a}=\frac{-7\pm \sqrt{56k^{2}}}{2}=\frac{-7\pm2k \sqrt{14}}{2}$
Since √14 is an irrational number, therefore any value of k will give an irrational number only. Therefore, the given equation has no integral roots. Hence option (3)