Advertisements
Advertisements
प्रश्न
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Advertisements
उत्तर १
Let the breadth of mango grove be l.
Length of mango grove will be 2l.
Area of mango grove = (2l) (l) = 2l2
2l2 = 800
l2 = `800/2`
l2 = 400
l2 - 400 = 0
Comparing this equation with al2 + bl + c = 0, we get
a = 1, b = 0, c = 400
Discriminant = b2 - 4ac = (0)2 - 4 × (1) × (- 400)
= 1600
Here, b2 - 4ac > 0
Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.
l = ±20
However, length cannot be negative.
Therefore, breadth of mango grove = 20 m
Length of mango grove = 2 × 20 = 40 m
उत्तर २
Let the breadth of the rectangular mango grove be x meter and the length 2x meters. Then
Area of the rectangle
length x breadth = 800
x(2x) = 800
2x2 = 800
x2 = 400
x = `sqrt400`
x = `+-20`
Sides of the rectangular hall never be negative.
Therefore, length
2x = 2(20) = 40
Yes, it is possible.
Hence, breadth of the hall be 20 meters and length be 40 meters.
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
`10x -(1)/x` = 3
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
Which of the following equations has two distinct real roots?
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
