List of top Quantitative Aptitude Questions on Quadratic Equations

If a,b,c are real numbers then the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
If α,β are the roots of x²-2x-1=0, then the value of α²β²-α²-β² is
If a,b are non-zero roots of x²+ax+b=0, then the least value of x²+ax+b is
The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are
If the equations \( x^2 + ax + 1 = 0 \) and \( x^2 - x - a = 0 \) have a real common root, then the value of \( b \) is
The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are
If the equations \( x^2 + ax + 1 = 0 \) and \( x^2 - x - a = 0 \) have a real common root, then the value of \( b \) is
The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are
If the equations \( x^2 + ax + 1 = 0 \) and \( x^2 - x - a = 0 \) have a real common root, then the value of \( b \) is
Let \( f(x) = px^2 + qx + r \), where \( p,q,r \) are constants and \( p \neq 0 \). If \( f(5) = -3f(2) \) and \( f(-4) = 0 \), then the other root of \( f \) is
The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are
If the equations \( x^2 + ax + 1 = 0 \) and \( x^2 - x - a = 0 \) have a real common root, then the value of \( b \) is
Let \( f(x) = px^2 + qx + r \), where \( p,q,r \) are constants and \( p \neq 0 \). If \( f(5) = -3f(2) \) and \( f(-4) = 0 \), then the other root of \( f \) is
If α,β are the roots of the equation x²-2x-1=0, then the value of α²β²+α-α²β² is
If a,b,c are real numbers then the roots of (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always