Assertion (A): The minimum possible complex roots of the equation x6 - 3x5 + 4x3 + 3x2 + 4 = 0 is 2. Reason (R): The equation x6 -3x5 + 4x3 + 3x2 + 4 = 0 has maximum four real roots.

Question

Assertion (A): The minimum possible complex roots of the equation x6 - 3x5 + 4x3 + 3x2 + 4 = 0 is 2. Reason (R): The equation x6 -3x5 + 4x3 + 3x2 + 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

Tardigrade Admin · Accepted Answer

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.

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

Both (A) & (R) are individually true & (R) is correct explanation of (A)

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A)

(A) is true but (R) is false

(A) is false but (R) is true

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.

Q. Assertion (A) : The minimum possible complex roots of the equation x6−3x5+4x3+3x2+4=0 is 2. Reason (R) : The equation x6−3x5+4x3+3x2+4=0 has maximum four real roots.