Question

Assertion (A) : If $\alpha, \beta$ are roots of the equation $3x^2 - 1 1x + 19 = 0$, then it is possible to find the value of $\alpha^3 + \beta^3$.
Reason (R) : Any symmetric function of roots can be expressed in term of elementary symmetric functions $S = \alpha + \beta, P = \alpha \beta$.

• 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)

We can write, $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha \,\beta (\alpha + \beta)$,
so Assertion (A) is true.
Reason (R) is true and correct explanation of Assertion (A).