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

Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.

Find the value of k for which the given equation has real roots:
kx² - 6x - 2 = 0

Find the value of k for which the given equation has real roots:
9x² + 3kx + 4 = 0.

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x² + 2x - 1 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a²b²x² - 48abc + 64c²d² = 0, a ≠ 0, b ≠ 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² - 5x + 7 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² - 4x + 1 = 0

Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x² + 5x + 15 = 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.

x² + 2(m – 1)x + (m + 5) = 0

Solve the following by reducing them to quadratic equations:
x⁴ - 26x2 + 25 = 0

Solve the following by reducing them to quadratic equations:
z⁴ - 10z² + 9 = 0.

Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.

Solve for x: (x² - 5x)² - 7(x² - 5x) + 6 = 0; x ∈ R.

Determine whether the given quadratic equations have equal roots and if so, find the roots:
x² + 5x + 5 = 0

Determine whether the given quadratic equations have equal roots and if so, find the roots:
x² + 2x + 4 = 0

Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`

Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x² - 6x + 5 = 0

Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx² + 6x - 3k = 0, k ≠ 0

Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x² + (2k + 1)x - 9 = 0, k + 1 ≠ 0.