List of top Mathematics Questions on Quadratic Equations asked in WBJEE

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
Consider a quadratic equation ax2+2bx+c=0 where a,b,c are positive real numbers. If the equation has no real root, then which of the following is true?
If one root of \(x^2+px-q^2=0\), p and q are real, be less than 2, and other be greater than 2. Then 
If $a$, $b$ are odd integers, then the roots of the equation $2ax^2 + (2a + b)x + b = 0$, where $a \neq 0$, are
The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2)x - (a - 1) = 0$ assumes the least value is
Let a, b, c be real numbers such that $a + b + c < 0$ and the quadratic equation $ax^2 + bx + c = 0$ has imaginary roots. Then
The roots of the quadratic equation $x^{2}-2\sqrt{3}x-22 = 0 $ are :
The area enclosed between y2 = x and y = x is
If p + q + r = a + b + c = 0, then the determinant Δ=|paqbrcqcrapbrbpcqa| equals
If a→=i^+2j^+3k^ and b→=i^×(a→×i^)+j^×(a→×j^)+k→×(a→×k^) then length of b→ isequal to
 The sequence log⁡ a, log⁡a2b,log⁡a3b2,……… is 
The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is 
The general solution of the differential equation loge⁡(dydx)=x+y is