If $a,\ b$ and $c$ are distinct positive real numbers in AP, then the roots of the equation $ax^{2} + 2bx + c = 0$ are

Question

Dr. Abubacker · Accepted Answer

(c)
Since, $b = \frac{a + c}{2}$ ...(i)
Now, discriminant, $D = B^{2} - 4AC$
$= 4b^{2} - 4ac$
$= 4\left( \frac{a + c}{2} ight)^{2} - 4ac$ [from Eq. (i)]
$= (a - c)^{2} \geq 0$
$	herefore$ Roots of the given equation are rational and distinct

Q. If $a,\ b$ and $c$ are distinct positive real numbers in AP, then the roots of the equation $ax^{2} + 2bx + c = 0$ are

Explanation

Reviewed by Dr. Abubacker

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