If the ratio of the roots of the quadratic equation $2 x^{2} + 16 x + 3 k = 0$ is $4 : 5$ then $k =$

$\frac{2560}{243}$
$\frac{243}{2560}$
$- \frac{2560}{243}$
$- \frac{243}{2560}$

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Solution

The correct option is A
$\frac{2560}{243}$

Find the value of $k$ :
$2 x^{2} + 16 x + 3 k = 0$
Suppose $ɑ, β$ be the roots of the given equation.
$\Rightarrow$ $(ɑ + β) = - 8, ɑ β = \frac{3 k}{2} a n d ɑ : β = 4 : 5$
$\Rightarrow$ $ɑ = 4 m, β = 5 m$
$\Rightarrow$ $(ɑ + β) = - 8$
$\Rightarrow$ $9 m = - 8$
$\Rightarrow$ $m = - \frac{8}{9}$
$\Rightarrow$ $ɑ = - \frac{32}{9}, β = - \frac{40}{9}$
$\Rightarrow$ $ɑ β = \frac{3 k}{2}$
$\Rightarrow$ $k = \frac{2560}{243}$
So, the option (A) is correct.

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If the ratio of the roots of the quadratic equation 2x2+16x+3k=0is 4:5 thenk=25602432432560-2560243-2432560

The correct option is A 2560243Find the value of k:2x2+16x+3k=0Suppose ɑ,β be the roots of the given equation.⇒ (ɑ+β)=–8,ɑβ=3k2andɑ:β=4:5⇒ ɑ=4m,β=5m⇒ (ɑ+β)=–8⇒ 9m=–8⇒ m=–89⇒ ɑ=–329,β=–409⇒ ɑβ=3k2⇒ k=2560243So, the option (A) is correct.

If the ratio of the roots of the quadratic equation $2 x^{2} + 16 x + 3 k = 0$ is $4 : 5$ then $k =$

$\frac{2560}{243}$
$\frac{243}{2560}$
$- \frac{2560}{243}$
$- \frac{243}{2560}$