List of top Mathematics Questions on Quadratic Equations asked in UP Board X

The roots of the quadratic equation $x^2 + 5x + 6 = 0$ will be :
Find the value of \( k \) for which the quadratic equation \( 2x^2 + kx + 3 = 0 \) has two equal real roots.
If the roots of the equation $x^2+2(m-1)x+(m+5)=0$ are real and equal, find the value of $m$.
Find two consecutive positive integers, sum of whose squares is $365$.
The area of a rectangular field is $30 \, m^2$. If its length is $1 \, m$ greater than its breadth $x$, then the quadratic equation to find them will be:
If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:

The discriminant of the quadratic equation $3x^2 - 4\sqrt{3}\,x + 4 = 0$ will be:
 

The length of a rectangular field is 9 m more than the twice of its width. If the area of the field is $810 \, m^2$, find the length and width of the field.
The zeroes of quadratic polynomial $6x^2 - 7x - 3$ will be:
Solve the quadratic equation \(2x^2 - 5x + 3 = 0\).
A train covers a distance of 180 km at a uniform speed. If the speed had been 5 km/hour more, then it would have taken $\dfrac{1}{2}$ hour less for the same journey. Find the speed of the train.
The discriminant of the quadratic equation $x^2 + x - 1 = 0$ will be
The sum of the roots of the quadratic equation $1 - 4x + 4x^2 = 0$ will be
If the roots of the equation \(3x^2 + 5x - q = 0\) are equal, then the value of \(q\) will be
If the equation $x^2 - 4x + a = 0$ has no real roots, then
The shape of the graph of a quadratic equation $y = ax^2 + bx + c$, $a \neq 0$, will be
Find the roots of the quadratic equation \(3x^2 - 2\sqrt{6}x + 2 = 0\).
Find the roots of the quadratic equation \(4x^2 + 9x + 5 = 0.\)
The nature of roots of the equation \(2x^2 + 5x + 4 = 0\) will be
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
The nature of the roots of the equation \( 2x^2 - 5x + 4 = 0 \) will be:
If one root of quadratic equation \( x^2 + 2x - p = 0 \) is \(-2\), then the value of \( p \) will be:
Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.
If one root of the equation \( x^2 - kx - 8 = 0 \) is 2, then the value of \( k \) will be:
The sum of the zeroes of the quadratic polynomial \( 4x^2 - 4x + 1 \) will be: