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Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
Concept: Nature of Roots of a Quadratic Equation
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
Concept: Nature of Roots of a Quadratic Equation
The roots of quadratic equation x2 – 1 = 0 are ______.
Concept: Nature of Roots of a Quadratic Equation
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
Concept: Miscellaneous Problems
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
Concept: Problems Based on Distance, Speed and Time
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
Concept: Problems Based on Numbers
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more, then each would have got Rs. 12 less. Find ‘x’.
Concept: Miscellaneous Problems
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.
Concept: Problems Based on Distance, Speed and Time
A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.
Concept: Problems Based on Distance, Speed and Time
The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:
| Distance (in m) | 60 | 90 | y |
| Time (in sec) | 2 | x | 5 |
The values of x and y are:
Concept: Problems Based on Distance, Speed and Time
A car travels a distance of 72 km at a certain average speed of x km per hour and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.
Concept: Problems Based on Distance, Speed and Time
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
Concept: Proportion
If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b
Concept: Ratio
The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series
Concept: Ratio
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Concept: Proportion
Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find
- x
- length of AP.
Concept: Ratio
If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.
Concept: Ratio
What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Concept: Proportion
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
Concept: Proportion
The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs. 80 every month, find their monthly pocket money.
Concept: Ratio
