If (2-3 i) is a root of the equation x3-b x2+25 x+d=0 (where b and d are real and i=√-1 ), then value of b is equal to

Question

If (2-3 i) is a root of the equation x3-b x2+25 x+d=0 (where b and d are real and i=√-1 ), then value of b is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

If one root is 2-3 i, then other root is 2+3 i sum of roots =b=α+2-3 i+2+3 i =4+α.....(i) sum of pair of roots =25 =(2-3 i)(2+3 i)+α(2-3 i)+α(2+3 i)=13+4 α =13+4 α ⇒ α=3 .....(ii) Using (i) and (ii) ⇒ b=7

Q. If $(2 - 3 i)$ is a root of the equation $x^{3} - b x^{2} + 25 x + d = 0$ (where $b$ and $d$ are real and $i = - 1$ ), then value of $b$ is equal to

If one root is $2 - 3 i$ , then other root is $2 + 3 i$
sum of roots $= b = α + 2 - 3 i + 2 + 3 i$
$= 4 + α$ .....(i)
sum of pair of roots $= 25$
$= (2 - 3 i) (2 + 3 i) + α (2 - 3 i) + α (2 + 3 i) = 13 + 4 α$
$= 13 + 4 α$
$\Rightarrow α = 3$ .....(ii)
Using (i) and (ii) $\Rightarrow b = 7$

Q. If (2−3i) is a root of the equation x3−bx2+25x+d=0 (where b and d are real and i=−1​ ), then value of b is equal to

If one root is 2−3i, then other root is 2+3i sum of roots =b=α+2−3i+2+3i =4+α.....(i) sum of pair of roots =25 =(2−3i)(2+3i)+α(2−3i)+α(2+3i)=13+4α =13+4α ⇒α=3 .....(ii) Using (i) and (ii) ⇒b=7

Q. If $(2 - 3 i)$ is a root of the equation $x^{3} - b x^{2} + 25 x + d = 0$ (where $b$ and $d$ are real and $i = - 1$ ), then value of $b$ is equal to

If one root is $2 - 3 i$ , then other root is $2 + 3 i$
sum of roots $= b = α + 2 - 3 i + 2 + 3 i$
$= 4 + α$ .....(i)
sum of pair of roots $= 25$
$= (2 - 3 i) (2 + 3 i) + α (2 - 3 i) + α (2 + 3 i) = 13 + 4 α$
$= 13 + 4 α$
$\Rightarrow α = 3$ .....(ii)
Using (i) and (ii) $\Rightarrow b = 7$