Question 2 :
State True or False whether the following quadratic equation has two distinct real roots : $\left(x-\sqrt{2}\right)^2-2\left(x+1\right)=0$
Question 3 :
Sum of the areas of two squares is $468 m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.
Question 4 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is
Question 5 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$
Question 6 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$
Question 8 :
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Write an equation to find out the number of toys produced on that day.
Question 11 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 – 7x + 3 = 0$
Question 12 :
Find the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$.
Question 13 :
Check whether the following is quadratic equation : $(x+1)^2 = 2(x-3)$
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b60273b23058497998d.png' />
In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the length of the pond.
Question 15 :
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Find out at what distances from the two gates should the pole be erected?
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998e.png' />
In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the breadth of the pond.
Question 17 :
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Question 18 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.
Question 20 :
Find the roots of the following quadratic equation (by the factorisation method): $21x^2-2x+\frac{1}{21}=0$
Question 21 :
Is it possible to design a rectangular park of perimeter 80 m and area $400 m^2$ ? If so, find its length and breadth.
Question 22 :
Does the following equation has the sum of its roots as 3? $-x^2+3x-3=0$
Question 27 :
What is the general expression (standard form) for quadratic equations ?
Question 28 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$
Question 29 :
State True or False: Every quadratic equation has at least two roots.
Question 30 :
Check whether the following is a quadratic equation: $x(x + 1) + 8 = (x + 2) (x – 2)$
Question 31 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 32 :
Justify why the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$
Question 33 :
State True or False: If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of $x$ term is zero, then the quadratic equation has no real roots.
Question 34 :
What are the roots of the quadratic equation $2x^2-\sqrt{5}x-2=0$ using the quadratic formula.
Question 35 :
Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$
Question 36 :
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Find out the number of toys produced on that day.
Question 37 :
A quadratic equation $ax^2 + bx + c =0$ has no real roots when :
Question 38 :
Using method of completing the square , solve for x: $4x^2+3x+5=0$
Question 39 :
Find the nature of the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$
Question 40 :
Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. The marks scored by her are?
Question 41 :
Using method of completing the square , $3x^2-5x+2=0$ can be written as ?
Question 42 :
State True or False: Every quadratic equation has exactly one root.
Question 43 :
Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$
Question 44 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2-6x+\frac{9}{2}=0$
Question 45 :
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the passenger train.
Question 46 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.
Question 47 :
Find the discriminant of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 49 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$
Question 50 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$
