If m is chosen in the quadratic equation (m2 + 1) x2 - 3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

Question

If m is chosen in the quadratic equation (m2 + 1) x2 - 3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is : (A)  8 √3 (B)  4 √3 (C) 10 √5 (D) 8 √5

Tardigrade Admin · Accepted Answer

SOR = (3/m2 +1) ⇒ (S.O.R)max = 3 when m = 0 α+β=3 αβ = 1 |α2 -β2| =| |α-β|(α2 + β2 +αβ) | = |√(α-β)2-αβ ((α+β)2 -αβ)| = |√9-4 (9-1)| = √5 ×8

Q. If $m$ is chosen in the quadratic equation $(m^{2} + 1) x^{2} - 3 x + (m^{2} + 1)^{2} = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

$83$

$43$

$105$

$85$

Q. If m is chosen in the quadratic equation (m2+1)x2−3x+(m2+1)2=0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

83​

43​

105​

85​

SOR=m2+13​⇒(S.O.R)max​=3 when m=0 α+β=3 αβ=1 ∣∣​α2−β2∣∣​=∣∣​∣α−β∣(α2+β2+αβ)∣∣​ =∣∣​(α−β)2−αβ​((α+β)2−αβ)∣∣​ =∣∣​9−4​(9−1)∣∣​ =5​×8

Q. If $m$ is chosen in the quadratic equation $(m^{2} + 1) x^{2} - 3 x + (m^{2} + 1)^{2} = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

$83$

$43$

$105$

$85$