List of top Quantitative Aptitude Questions on Quadratic Equation asked in CAT

The quadratic equation \(x^2+bx+c=0\) has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of \(b^2+c\ ?\)

If x is a real number, then \(\sqrt{log_e\frac{4x-x^2}{3}}\)  is a real number if and only if

Let a, b, x, y be real numbers such that \(a^2+b^2=25,x^2+y^2=169,\) and \(ax+by=65.\) If \(k= ay-bx,\) then

If the roots of the equation \( x^2 - 2px + p^2 - 1 = 0 \) are real and distinct, what is the range of \( p \)?

Find the roots of $x^2 - 8x + 15 = 0$.

If $x^2 - 7x + 12 = 0$, what is the value of $x^3 - 4x^2 + 3x$?

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \[ x^2 - 10x + 15 = 0, \] then find the quadratic equation whose roots are \( \left( \alpha + \frac{\alpha}{\beta} \right) \) and \( \left( \beta + \frac{\beta}{\alpha} \right) \).

If \( ax^2 + bx + c = 0 \) and \( 2a, b, 2c \) are in arithmetic progression, then which of the following are the roots of the equation?

If the roots of the equation \[ (a^2 + b^2)x^2 + 2(b^2 + c^2)x + (b^2 + c^2) = 0 \] are real, which of the following must hold true?

The ratio of the roots of \( bx^2 + nx + n = 0 \) is \( p:q \), then

A quadratic function \( f(x) \) attains a maximum of 3 at \( x = 1 \). The value of the function at \( x = 0 \) is 1. What is the value \( f(x) \) at \( x = 10 \)?

Let \( f(x) = ax^2 - b |x| \), where \(a\) and \(b\) are constants. Then at \(x = 0\), \(f(x)\) is

Let f(x) = ax² + bx + c, where a, b, and c are real numbers with a ≠ 0. If the graph of f(x) intersects the x-axis at two distinct points with x-coordinates p and q (p < q), then the equation ax² + bx + c + 1 = 0 has: