If one root of the equations ax2 + bx + c = 0 and bx2 + cx + a = 0 (a, b, c ∈ R) is common, then the value of ((a3 + b3 + c3/abc)) is

Question

If one root of the equations ax2 + bx + c = 0 and bx2 + cx + a = 0 (a, b, c ∈ R) is common, then the value of ((a3 + b3 + c3/abc)) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Applying condition for common root, we get a3 + b3 + c3 = 3abc ⇒ ((a3 + b3 + c3/abc)) = 27

Q. If one root of the equations $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0 (a, b, c \in R)$ is common, then the value of $(\frac{a ^{3} + b ^{3} + c ^{3}}{ab c})$ is

Applying condition for common root, we get
$a^{3} + b^{3} + c^{3} = 3 ab c$
$\Rightarrow (\frac{a ^{3} + b ^{3} + c ^{3}}{ab c}) = 27$

Q. If one root of the equations ax2+bx+c=0 and bx2+cx+a=0(a,b,c∈R) is common, then the value of (abca3+b3+c3​) is

Applying condition for common root, we get a3+b3+c3=3abc ⇒(abca3+b3+c3​)=27

Q. If one root of the equations $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0 (a, b, c \in R)$ is common, then the value of $(\frac{a ^{3} + b ^{3} + c ^{3}}{ab c})$ is

Applying condition for common root, we get
$a^{3} + b^{3} + c^{3} = 3 ab c$
$\Rightarrow (\frac{a ^{3} + b ^{3} + c ^{3}}{ab c}) = 27$