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List of top Mathematics Questions on Quadratic Equations

If the equation \( \sin^4 x - (p + 2)\sin^2 x - (p + 3) = 0 \) has a solution, then \( p \) must lie in the interval:
If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then
For what value of \( 'a' \), the sum of the squares of the roots of the equation \( x^2 - (a - 2)x - a + 1 = 0 \) will have the least value?
If the sum of the squares of the roots of the equation $x^2 - (a-2)x - (a+1) = 0$ is least for an appropriate value of the variable parameter $a$, then that value of $a$ will be
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) are real and distinct, what is the range of values for \( k\)?
If the roots of the quadratic equation \( 2x^2 - 5x + k = 0 \) are real and distinct, what is the range of values for \( k \)?
The roots of the equation \( x^2 + 5x + 6 = 0 \) are:

If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and equal, then:

If one root of the quadratic equation \( ax^2 + bx + c = 0 \) is double the other, then what is the correct relation among the coefficients?
The quadratic equation $ x^2 - 5x + k = 0 $ has equal roots. Find the value of $ k $.
If $ f(x) = x^2 + 3x $, then $ f'(x) $ is:
If the roots of the quadratic equation $ x^2 + 4x + k = 0 $ are real and equal, then the value of $ k $ is:
The ratio of the sum of two numbers to their difference is 5:1. If the sum of the numbers is 18, find the numbers.
Find the solution of the quadratic equation \( 2x^2 - 3x - 5 = 0 \).
Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x+2} = \frac{5}{6} \).
The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:
If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: