IGNOU MTE 4 2018 - Obtain the discriminant of the equation 2x3 − 23x2 + 82x −

Question

Obtain the discriminant of the equation 2x³− 23x² + 82x − 78 = 0 . Hence provide the nature of its roots.

02 Feb 2018

Answer :

Word Count : 332

We are asked to determine the discriminant of the cubic equation: $$ 2x^3 - 23x^2 + 82x - 78 = 0 $$ and then deduce the nature of its roots. --- For a cubic equation $ax^3 + bx^2 + cx + d = 0$, the discriminant $\Delta$ is given by: $$ \Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2 $$ Here, $a = 2$, $b = -23$, $c = 82$, $d = -78$. Step by step: 1. Compute each term: * $18abcd = 18 \cdot 2 \cdot (-23) \cdot 82 \cdot (-78)$ Stepwise: $2 \cdot (-23) = -46$ $-46 \cdot

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