Aarav is designing a rectangular kitchen garden in Pune. Its length is 3 m more than its width, and he claims the area is exactly 7 sq m. If the width is x metres, the equation becomes x^2 + 3x - 7 = 0. What is the nature of the roots, and is such a garden possible?

Question

Accepted Answer

Real and distinct, so it is possible. D = 9 - 4(1)(-7) = 9 + 28 = 37 > 0, so the roots are real and distinct; a valid positive width exists, so the garden is possible.

Aarav is designing a rectangular kitchen garden in Pune. Its length is 3 m more than its width, and he claims the area is exactly 7 sq m.
If the width is $x$ metres, the equation becomes $x^{2} + 3 x - 7 = 0$ .
What is the nature of the roots, and is such a garden possible?

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More Class 10 Nature of Roots (Discriminant) practice

Aarav is designing a rectangular kitchen garden in Pune. Its length is 3 m more than its width, and he claims the area is exactly 7 sq m.If the width is x metres, the equation becomes x2+3x−7=0.What is the nature of the roots, and is such a garden possible?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Nature of Roots (Discriminant) practice

Aarav is designing a rectangular kitchen garden in Pune. Its length is 3 m more than its width, and he claims the area is exactly 7 sq m.
If the width is $x$ metres, the equation becomes $x^{2} + 3 x - 7 = 0$ .
What is the nature of the roots, and is such a garden possible?