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NTPC Graduate Tier 1 2025 Shift-3 📅 06 Jun, 2025

Sum and product of all roots of $4x^{3}-8x^{2}-13x+19=0$ is:

A

4, -19/2

B

1, -17/4

C

3, -17/2

D

2, -19/4

Result Summary

APEDIA

NTPC Graduate Tier 1

2025 • 06 Jun, 2025 • Shift-3

Sum and product of all roots of $4x^{3}-8x^{2}-13x+19=0$ is:

Correct Answer

2, -19/4

Vieta's Formulas Application: For a cubic equation of the form $ax^3 + bx^2 + cx + d = 0$, Vieta's formulas state that the sum of the roots is $-b/a$ and the pr......

💡 Analysis & Explanation

Vieta's Formulas Application ▼

For a cubic equation of the form $ax^3 + bx^2 + cx + d = 0$, Vieta's formulas state that the sum of the roots is $-b/a$ and the product of the roots is $-d/a$.

Extracting Coefficients ▼

In the given equation $4x^3 - 8x^2 - 13x + 19 = 0$, we have $a=4$, $b=-8$, $c=-13$, and $d=19$.

Calculating Sum and Product ▼

The sum of the roots is $-(-8)/4 = 8/4 = 2$. The product of the roots is $-(19)/4 = -19/4$.

Conclusion ▼

Therefore, the sum is 2 and the product is -19/4.