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.
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
A quadratic equation with integral coefficient has integral roots. Justify your answer.
Write whether the statement are true or false. Justify your answer.
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
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