Question

Assertion (A) : The minimum possible complex roots of the equation $x^6 - 3x^5 + 4x^3 + 3x^2 + 4 = 0$ is 2.
Reason (R) : The equation $x^6 -3x^5 + 4x^3 + 3x^2 + 4 = 0$ has maximum four real roots.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A)
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A)
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Answer 1

Answer: (A)

Since $f(x)$ has two changes in sign and $f(- x)$ has too, two changes in sign. Hence the maximum number of real roots is 4 and hence the equation has at least (minimum) two complex roots.