If a, b, c are distinct positive real numbers such that b(a + c) = 2ac then the roots of $a x^{2} + b x + c = 0$ are

real and equal

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real and distinct

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Imaginary

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data insufficient

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Solution

The correct option is C
Imaginary

$b = \frac{2 a c}{a + c} \Rightarrow$ b is HM of a & c.
$\Rightarrow a x^{2} + 2 b x + c = 0 ∴ Δ = 4 b^{2} - 4 a c = 4 (b^{2} - a c)$
GM of a & c is $\sqrt{a c}$
$∴ a c > b^{2} (G M \geq H M) ∴ Δ < 0$

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Similar questions

If a, b, c are distinct positive real numbers such that b(a + c) = 2ac then the roots of $a x^{2} + b x + c = 0$ are

If a,b,c are distinct positive real numbers such that b(a+c) = 2ac then the roots a $x^{2}$ + 2bx + c = 0 are :

\neq

a x^{2}

a x^{2}

a, b, c

a x^{2} + 2 b | x | - c = 0

α, β

a x^{2} + b x - c = 0

p, q

a x^{2} + b x - | c | = 0

(a > 0)

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