quadratic equations Questions

Which of the following quadratic equations has equal roots?

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$, then find the two numbers?

A group of $630$ children seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?

If 3sec
4
θ+8=10sec
2
θ, then the value of tanθ can be:

Som is slower than Ram, and each travels 150 km. The sum of their speeds is 25 km/h and the sum of the time taken by them is 25 hours. Then, Som's speed is:

If 4sin
2
θ−4
3

​
sinθ+3=0, then find the value of θ (0
∘
<θ<90
∘
).

The addition of a rational number and its reciprocal is $\frac{74}{35}$. Calculate the number.

If $(x-1)$ is a factor of $x^2-7qx+12q=0$, then find the possible values of $q$.

The number of coconuts plucked from each tree is $1$ more than the total number of coconut trees in Anil's garden. If the total number of coconuts plucked is $132$, find the total number of coconut trees in the garden.

The square of a number is $48$ more than $22$ times of itself. Find the number.

If the product of two successive positive integers is $7482$, which is the greatest integer?

What value of $m$ ensures that the two roots of the quadratic equation $4x^2+4(3m-1)x+(m+7)=0$ are reciprocal to each other?

If $\alpha$ and $\beta$ are the roots of the quadratic equation $a{x}^2+2bx+c=0$ and $\alpha +\gamma$, $\beta +\gamma$ are the roots of $A{x}^2+2Bx+C=0$, then which one of the following is correct?

Ram and Shyam solve a quadratic equation. Ram makes a mistake in the constant term and finds the roots as $5,-3$. Shyam makes a mistake in the co-efficient of $x$ and gets the roots as $1,-3$. The correct roots are:

If the current ratio of the father's age to the son's age is $4:1$ and the product of their ages is $256$, what will be the ratio of their ages after $5$ years?

Solve the following equation for $x$:
$$\frac{1}{x+1}+\frac{2}{x+5}=\frac{1}{2}$$