First slide

Theory of equations

Question

If a and b are the odd integers, then the roots of the equation $2 {ax}^{2} + (2 a + b) x + b = 0, a \neq 0, will be$

Moderate

A

Rational
B

Irrational
C

Non-real
D

Equal

Solution

Given equation $2 {ax}^{2} + (2 a + b) x + b = 0, (a \neq 0)$
Now its discriminant $D = B^{2} - 4 AC$
$= {(2 a + b)}^{2} - 4.2 ab = {(2 a - b)}^{2}$
Hence D is a perfect square, so given equation has rational roots.

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