Ramesh wants to build a rectangular vegetable garden whose length is 3 m more than its width. If the area is to be exactly 40 sq m, he models it as x^2 + 3x - 40 = 0 where x is the width. Using the discriminant, what is the nature of the roots of this equation?

Question

Accepted Answer

Real and distinct. a = 1, b = 3, c = -40. D = 9 + 160 = 169 > 0, so the roots are real and distinct. (The positive root x = 5 m gives a valid width.)

Ramesh wants to build a rectangular vegetable garden whose length is 3 m more than its width. If the area is to be exactly 40 sq m, he models it as $x^{2} + 3 x - 40 = 0$ where $x$ is the width.
Using the discriminant, what is the nature of the roots of this equation?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Discriminant and Nature of Roots practice

Ramesh wants to build a rectangular vegetable garden whose length is 3 m more than its width. If the area is to be exactly 40 sq m, he models it as x2+3x−40=0 where x is the width.Using the discriminant, what is the nature of the roots of this equation?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Discriminant and Nature of Roots practice

Ramesh wants to build a rectangular vegetable garden whose length is 3 m more than its width. If the area is to be exactly 40 sq m, he models it as $x^{2} + 3 x - 40 = 0$ where $x$ is the width.
Using the discriminant, what is the nature of the roots of this equation?