Maharashtra Board Solutions for Chapter: Quadratic Equations, Exercise 7: Problem Set

Solve the quadratic equation $x^2-4x-3=0$

Find $m$ if $(m-12)x^2+2(m-12)x+2=0$ has real and equal roots.

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation $2x^2+2\left(p+q\right)x+p^2+q^2=0$

Mukund possesses $₹50$ more than what Sagar possesses. The product of the amount they have is $₹15,000$. Find the amount each one has.

The difference between squares of two numbers is $120$. The square of smaller number is twice the greater number. Find the numbers.

Ranjana wants to distribute $540$ oranges among some students. If $30$ students were more each would get $3$ oranges less. Find the number of students.

Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is $10 \mathrm{m}$ more than twice the breadth. In order to harvest rainwater, he dug a square shaped pond inside the farm. The side of pond is $\frac{1}{3}$ of the breadth of the farm. The area of the farm is $20$ times the area of the pond. Find the length and breadth of the farm and length of the pond.

A tank fills completely in $2$ hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes $3$ hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?