Question Text
Question 1 :
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.
Question 2 :
Find the roots of the following quadratic equation (by the factorisation method): $3\sqrt{2}x^2-5x-\sqrt{2}=0$
Question 4 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$
Question 5 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x + 4 = 0$
Question 6 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced.
Question 7 :
State True or False: If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Question 9 :
Check whether the following is quadratic equation : (2x- 1)(x -3)=(x +5)(x -1)
Question 10 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.