If the roots of cubic equation x3-6 x2+k x-8=0 are positive real numbers, then find the value of ( k -7)

Question

If the roots of cubic equation x3-6 x2+k x-8=0 are positive real numbers, then find the value of ( k -7) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/681256fd9f328f612d1cd5954d2d939b-.png" /> Arithmetic mean of roots =2 Geometric mean of roots =2 ⇒ α=β=&gamma;=2 text So, k=12 ⇒ k-7=5

Q. If the roots of cubic equation $x^{3} - 6 x^{2} + k x - 8 = 0$ are positive real numbers, then find the value of $(k - 7)$

Arithmetic mean of roots $= 2$
Geometric mean of roots $= 2$
$\Rightarrow α = β = γ = 2$
$So, k = 12 \Rightarrow k - 7 = 5$

Q. If the roots of cubic equation x3−6x2+kx−8=0 are positive real numbers, then find the value of (k−7)

Arithmetic mean of roots =2 Geometric mean of roots =2 ⇒α=β=γ=2 So, k=12⇒k−7=5

Q. If the roots of cubic equation $x^{3} - 6 x^{2} + k x - 8 = 0$ are positive real numbers, then find the value of $(k - 7)$

Arithmetic mean of roots $= 2$
Geometric mean of roots $= 2$
$\Rightarrow α = β = γ = 2$
$So, k = 12 \Rightarrow k - 7 = 5$