Assertion (A): If α, β are roots of the equation 3x2 - 1 1x + 19 = 0, then it is possible to find the value of α3 + β3. Reason (R): Any symmetric function of roots can be expressed in term of elementary symmetric functions S = α + β, P = α β.

Question

Assertion (A): If α, β are roots of the equation 3x2 - 1 1x + 19 = 0, then it is possible to find the value of α3 + β3. Reason (R): Any symmetric function of roots can be expressed in term of elementary symmetric functions S = α + β, P = α β. (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

We can write, α3 + β3 = (α + β)3 - 3α β (α + β), so Assertion (A) is true. Reason (R) is true and correct explanation of Assertion (A).

Q. Assertion (A) : If $α, β$ are roots of the equation $3 x^{2} - 11 x + 19 = 0$ , then it is possible to find the value of $α^{3} + β^{3}$ .
Reason (R) : Any symmetric function of roots can be expressed in term of elementary symmetric functions $S = α + β, P = α β$ .

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

We can write, $α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$ ,
so Assertion (A) is true.
Reason (R) is true and correct explanation of Assertion (A).

Q. Assertion (A) : If α,β are roots of the equation 3x2−11x+19=0, then it is possible to find the value of α3+β3. Reason (R) : Any symmetric function of roots can be expressed in term of elementary symmetric functions S=α+β,P=αβ.