A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
Find whether the equations have real roots. If real roots exist, find them
5x2 – 2x – 10 = 0
Find whether the equations have real roots. If real roots exist, find them.
-2x2 + 3x + 2 = 0
Find whether the equations have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?
Check whether the equation 6x2 – 7x + 2 = 0 has real roots, and if it has, find them by the method of completing the squares.
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
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