Question

The area of a rectangle is x^2+2x-24: Which of the following could be one of the dimensions?
(x-4)
(x+8)
(x-3)
(x-6)

Answer 1

Answer:

(x-6)

Step-by-step explanation:

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Answer 2

Concept:

The polynomial equations of degree two in one variable of type

f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).

The roots of the quadratic equation: x = (-b ± √D)/2a,

where

D = b² – 4ac

Nature of roots:

D > 0, roots are real and distinct (unequal)

D = 0, roots are real and equal (coincident)

D < 0, roots are imaginary and unequal

Given:

The area of a rectangle is x²+2x-24

Find:

We have to find which among the options will be one of the dimensions of the given equation (x-4), (x+8), (x-3), and(x-6).

Solution:

The area of a rectangle = x²+2x-24

                                       = x² + 6x- 4x - 24

                                       = x( x+6) -4(x+ 6)

                                       = (x-4) (x+6)

Hence, option (x-4) is one of the dimensions of a rectangle is x²+2x-24

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