(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x² + (p – 3)x + p = 0.

Find the value (s) of k for which each of the following quadratic equation has equal roots : kx² – 4x – 5 = 0

Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x² + 2(k – 4) x + 4 = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x² + 2(m + 1)x + m = 0

Find the values of k for which each of the following quadratic equation has equal roots: 9x² + kx + 1 = 0 Also, find the roots for those values of k in each case.

Find the values of k for which each of the following quadratic equation has equal roots: x² – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation (2p + 1)x² – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.

If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.

Find the value(s) of p for which the equation 2x² + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

Find the values of p for which the equation 3x² – px + 5 = 0 has real roots.

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x² + 2(m – 1) x + (m + 5) = 0

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:

1. the onward journey;
2. the return journey.

If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

Which of the following equations has 2 as a root?

If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.

Choose the correct answer from the given four options :

If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is

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The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)

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If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)

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If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are

Choose the correct answer from the given four options :

If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by