List of top Quantitative Aptitude Questions on Quadratic Equations

If $9^{x^2+2x-3} - 4\bigl(3^{x^2+2x-2}\bigr) + 27 = 0$, then the product of all possible values of $x$ is:
The equations $3x^2 - 5x + p = 0$ and $2x^2 - 2x + q = 0$ have one common root. The sum of the other roots of these two equations is:
If $a, b, c$ and $d$ are integers such that their sum is $46$, then the minimum possible value of $(a - b)^2 + (a - c)^2 + (a - d)^2$ is:
If \( x^2 + 2(K+2)x + 36 = 0 \) has equal roots, then \( K = \)
If \( -4 \) is a root of the equation \( x^2 + ax - 4 = 0 \) and the equation \( x^2 + ax + b = 0 \) has equal roots, then what will be the value of \( \sqrt{a^2 + b^2} \)?
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^2 + 5x + k = 0 \), and \( 4(\alpha^2 + \beta^2 + \alpha\beta) = 23 \), then which of the following is true?
If the roots of the equation \(x^2 - 2(1+3k)x + 7(3+2k) = 0\) are equal, where \(k<0\), then which of the following is true?
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 the roots of the equation \(x^2 - 2(1+3k)x + 7(3+2k) = 0\) are equal, where \(k<0\), then which of the following is true?
Which of the following statements is true about the solutions of the equation \(\lvert x^2 - 5x \rvert = 6\)?
Which of the following statements is true about the solutions of the equation \(\lvert x^2 - 5x \rvert = 6\)?
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?
If a,b are non-zero roots of x²+ax+b=0, then the least value of x²+ax+b is
Which one of the following is not a quadratic equation?
The set of real numbers which satisfy the equation \( x^2 - 5x + 6 = 0 \) is:
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
The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are
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 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