List of top Mathematics Questions on Quadratic Equations

If \( \alpha,\beta \) where \( \alpha<\beta \), are the roots of the equation \[ \lambda x^2-(\lambda+3)x+3=0 \] such that \[ \frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}, \] then the sum of all possible values of \( \lambda \) is:
Let $\alpha, \beta$ be the roots of the quadratic equation \[ 12x^2 - 20x + 3\lambda = 0,\ \lambda \in \mathbb{Z}. \] If \[ \frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}, \] then the sum of all possible values of $\lambda$ is
Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be \( 2 \) and \( \frac{293}{4} \), respectively. Then the mean of 4 numbers x, y, x+y+1, |x-y| is:
The sum of all the roots of the equation \((x-1)^2 - 5|x-1| + 6 = 0\), is:
If the system of equations \[ \begin{cases} 2x + y + pz = -1 \\ 3x - 2y + z = q \\ 5x - 8y + 9z = 5 \end{cases} \] has more than one solution, then \( q - p \) is equal to:
If \( 4x^2 + y^2<52 \), where \( x, y \in \mathbb{Z} \), then the number of ordered pairs \( (x,y) \) is:
If both the roots of the equation \[ x^2-2ax+a^2-1=0 \quad (a\in\mathbb{R}) \] lie in the interval \((-2,2)\), then the equation \[ x^2-(a^2+1)x-(a^2+2)=0 \] has:
A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.
If the arithmetic mean of \(\dfrac{1}{a}\) and \(\dfrac{1}{b}\) is \(\dfrac{5}{16}\) and \(a,\,4,\,\alpha,\,b\) are in increasing A.P., then both the roots of the equation \[ \alpha x^2-ax+2(\alpha-2b)=0 \] lie between:
The roots of the quadratic equation $x^2 + 5x + 6 = 0$ will be :
If \(\alpha, \beta\) are roots of the quadratic equation \[ \lambda x^2 - (\lambda+3)x + 3 = 0 \] and \(\alpha<\beta\) such that \[ \frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}, \] then find the sum of all possible values of \(\lambda\).
Let \(x=x(t)\) be the solution curve of the differential equation \[ \frac{dx}{dt}=-kx, \] with \[ x(0)=100,\quad x\!\left(\frac{1}{2}\right)=80. \] If \(x(t_\alpha)=5\), then \(t_\alpha\) is equal to:
Solve the quadratic equation $x^2 - 5x - 10 = 0$ and give your answer correct to two decimal places.
The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.
Let \(\alpha\) and \(\beta\) be the roots of the equation \[ 2x^2-5x-1=0. \] For \(n\in\mathbb{N}\), let \[ P_n=\alpha^n+\beta^n. \] Then the value of \[ \frac{2P_{11}\,(2P_{10}-5P_9)}{P_8\,(5P_{10}+P_9)} \] is equal to:
Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + 2ax + (3a + 10) = 0$ such that $\alpha<1<\beta$. Then the set of all possible values of $a$ is :
Form a quadratic equation, one of whose zero is \( 2 + \sqrt{5} \) and the sum of zeros is 4.
If the zeroes of a quadratic polynomial \( 3x^2 - kx + 12 \) are equal, then find the value of \( k \).
In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.
In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.
Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.
The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of \(k\) is
Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).
The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered \(2 \text{ m}\) extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?