Find the sum of the roots of the cubic equation $5 x^{3} - 12 x^{2} + 7 x - 2 = 0$ .

hard 4 marks Class 9 · Mathematics · Polynomials

Answer

\displaystyle\frac{12}{5}

The correct answer is \displaystyle\frac{12}{5} — Therefore the sum of the roots is $\frac{12}{5}$ .

Step-by-step solution

Recall Viète's formula: for a cubic $a x^{3} + b x^{2} + c x + d = 0$ , the sum of the roots is $- \frac{b}{a}$ .
Identify $a = 5$ and $b = - 12$ in the given equation.
Compute $- \frac{b}{a} = - \frac{- 12}{5} = \frac{12}{5}$ .
Therefore the sum of the roots is $\frac{12}{5}$ .

Common mistake: Using

\frac{b}{a}

instead of

- \frac{b}{a}

Concept tested: Sum of roots of cubic via Viète