Sum and product of all roots of 4x³ − 8x² − 13x + 19 = 0 is :

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)

Answer 1

Given:

The polynomial equation is 4x³ - 8x² - 13x + 19 = 0.

Formula used:

Sum of roots = -b/a

Product of all roots = (-1)ⁿ × constant term/a, where n is the degree of the polynomial.

Calculations:

For the polynomial 4x³ - 8x² - 13x + 19 = 0:

Coefficient of x³ (a) = 4

Coefficient of x² (b) = -8

Constant term = 19

Sum of roots:

⇒ Sum of roots = -b/a

⇒ Sum of roots = -(-8)/4 = 2

Product of all roots:

⇒ Product of all roots = (-1)³ × constant term/a

⇒ Product of all roots = -19/4

∴ Sum and product of all roots are 2 and -19/4 respectively.

The correct answer is option 2.

Download Solution PDF