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1. Solve the equation 2x ^ 3 + 7x ^ 2 - 10x - 24 = 0 in the real number system

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The solution to the given equation in the real number system is x = 2 or x = -4 or x = -3/2

What is a real number system?

A real number system comprises rational numbers, irrational numbers, integers, and whole numbers. When solving a polynomial in a real number system, we need to first factor the polynomial by grouping;

i.e.

= 2x³ + 7x ² - 10x - 24

= 2x³ + 11x² + 12x - 4x² - 22x - 24

= x(2x² + 11x + 12) - 2(2x² + 11x + 12)

= (x - 2) (2x² + 11x + 12)

= (x - 2) (2x² + 8x + 3x + 12)

= (x - 2) (2 (x² + 4x) + 3(x + 4))

= (x - 2) (2x (x + 4) + 3(x + 4) )

= (x - 2) (x + 4) (2x + 3)

In a real number system;

x = 2 or x = -4 or x = -3/2

Learn more about the real number system here:

https://brainly.com/question/540415

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