The discriminant of the quadratic equation 2x² – 3x – 5 = 0 is :
The difference of the squares of two positive numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.
Find the value(s) of k for which the equation 2x² + kx + 3 = 0 has real and equal roots. Hence, find the roots of the equations so obtained.
One of the values of 'p' for which px² + 4x + p = 0 has real and equal roots is :
It is given that p²x² + (p² - q²)x - q² = 0 ; (p ≠ 0) (i) Show that the discriminant (D) of above equation is a perfect square. (ii) Find the roots of the equation.
Three consecutive positive integers are such that the sum of the square of smallest and product of other two is 67. Find the numbers, using quadratic equation.
© 2026 PadhAiPro. This question is provided for educational purposes.
