List of top Quantitative Aptitude Questions on Quadratic Equation

If \(x+1\) is a factor of \(2x^3 + ax^2 + 2bx + 1\), then find the values of \(a\) and \(b\) given that \(2a - 3b = 4\).

Which of the following is a factor of \(x^3 - 19x + 30\)?

Let \(x, y, z\) be real numbers such that \(4(x^2 + y^2 + z^2) = a\) and \(4(x - y - z) = 3 + a\), then find the value of \(a\).

The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is

Given the equation \(x^2 - 5x = 6 - y^2 + 3y = 9y + 9\).
Quantity A: \(x\)
Quantity B: \(y\)

Given the equations:
\(x^2 + 5x - 24 = 0\)
\(y^2 - 9y + 20 = 0\)

Quantity A: x
Quantity B: y

One of the roots of the equation x² + kx - 12 = 0 is 3, and k is a constant.
Quantity A: The value of k
Quantity B: -1

The product of two consecutive positive integers is 272. What is the larger of the two integers?

The value of \(\frac{1}{x+1}+\frac{2x}{1-x^2}+\frac{x}{x-1}\) is :

Suppose one of the roots of the equation \(a x^2 - b x + c = 0 \) is \( 2 + \sqrt{3}\), where a, b and c are rational numbers and \(a ≠ 0\). If \(b = c^3\) then |a| equals

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

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

If \( \alpha \) 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 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

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the orginal quadratic equation?

What is the number of distinct terms in the expansion of $(x + y + z )25$ ?

If p, q, r and s are four positive integers such that pqrs = 1, what is the minimum value of (2 + p)(3 + q)(4 + r)(5 + s)?