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| 1. |
If a, b are odd integers, then the roots of the equation 2ax2 + (2a + b) x + b = 0, a ≠ 0 is : (a) non-real (b) equal (c) irrational (d) rational |
| Answer» <p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Correct option (d) rational</strong></span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Explanation:</strong></span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">Equation is 2ax<sup>2</sup> + (2a + b) x + b = 0 </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">Discriminant = (2a + b)<sup>2</sup> − 4 . 2a . b </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">= (2a + b)<sup>2</sup> − 8ab > 0 </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">∴ Roots are rational.</span></span></p> | |