Advertisements
Advertisements
प्रश्न
Represent the following situation in the form of a quadratic equation.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.
उत्तर
Let the speed of the train be x km/h.
Time taken to travel 480 km = 480/x km/h
In second condition, let the speed of train = (x − 8) km/h
It is also given that the train will take 3 hours to cover the same distance.
`480/x`
`480/(x - 8)`
`480/(x - 8) = 480/x + 3`
`480/(x - 8) - 480/x = 3`
`((480)(8))/((x - 8)(x)) = 3`
x2 − 8x − 1280 = 0
ax2 + bx + c = 0
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
x = `(8 ± sqrt(64 + 4(1280)))/2`
= `(8 ± 72)/2`
= 40 km/hr
APPEARS IN
संबंधित प्रश्न
If α + β = 5 and α3 +β3 = 35, find the quadratic equation whose roots are α and β.
(x + 5)(x - 2) = 0, find the roots of this quadratic equation
Represent the following situation in the form of a quadratic equation:
The product of two consecutive positive integers is 306. We need to find the integers.
Check whether the following is quadratic equation or not.
(2𝑥 + 1)(3𝑥 + 2) = 6(𝑥 − 1)(𝑥 − 2)
Solve : x² – 10x – 24 = 0
Solve the following equation using the formula:
x2 – 10x + 21 = 0
Solve for x using the quadratic formula. Write your answer correct to two significant figures.
(x – 1)2 – 3x + 4 = 0
Solve the following equation using the formula:
`(2x)/(x - 4) + (2x - 5)/(x - 3) = 8 1/3`
Without solving, comment upon the nature of roots of the following equation:
`x^2 + 2sqrt(3)x - 9 = 0`
Which of the following are quadratic equation in x?
`(x+2)^3=x^3-8`
`2x^2+ax-a^2=0`
`x^2-2ax(4b^2-a^2)=0`
`16/x-1=15/(x+1),x≠0,-1`
The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.
A train travels a distance of 300kms at a constant speed. If the speed of the train is increased by 10km/ hour, the j ourney would have taken 1 hour less. Find the original speed of the train.
Solve:
`3sqrt(2x^2) - 5x - sqrt2 = 0`
In each of the following find the values of k of which the given value is a solution of the given equation:
x2 - x(a + b) + k = 0, x = a
Solve the following equation by using formula :
(2x + 3)(3x – 2) + 2 = 0
Solve the equation 5x2 – 3x – 4 = 0 and give your answer correct to 3 significant figures:
Solve the following equation by using formula :
2x2 – 3x – 1 = 0
