Question 1 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.
Question 2 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 3 :
Represent the following situation in the form of quadratic equations : The area of a rectangular plot is $528 m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Question 4 :
Justify why the following quadratic equation has no two distinct real roots: $\left(x+4\right)^2-8x=0$
Question 6 :
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 7 :
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 cost of each article?
Question 8 :
Check whether the following is quadratic equation : $x^3 - 4x^2 - x + 1 = (x-2)^3$
Question 9 :
Check whether the following is quadratic equation : (x - 2)(x +1)=(x - 1)(x + 3)
Question 10 :
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Question 11 :
Check whether the following is a quadratic equation: $x^2 – 2x = (–2) (3 – x)$
Question 12 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$
Question 13 :
Check whether the following is a quadratic equation: $x^2 + 3x + 1 = (x – 2)^2$
Question 14 :
Find two numbers whose sum is 27 and product is 182.
Question 16 :
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 19 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.
Question 20 :
Find the roots of the following quadratic equation (by the factorisation method): $3\sqrt{2}x^2-5x-\sqrt{2}=0$
Question 21 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2-6x+\frac{9}{2}=0$
Question 23 :
Find the nature of the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$
Question 25 :
Find the roots of the quadratic equation (by using the quadratic formula): $-x^2+7x-10=0$
Question 26 :
Find the discriminant of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 27 :
What are the roots of $6x^2-\sqrt{2}x-2=0$ (by the factorisation of the corresponding quadratic polynomial)?
Question 28 :
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 express train.
Question 30 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$
Question 31 :
Check whether the following is a quadratic equation: $x(2x + 3) = x^2 + 1$
Question 32 : <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 33 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 34 :
A natural number, when increased by 12, equals 160 times its reciprocal. The number is ____
Question 36 :
State True or False: Every quadratic equation has at most two roots.
Question 37 :
State true or false:
A quadratic equation in the variable x is an equation of the form $ax^2 + bx + c = 0$, where a, b and c are real numbers and a≠ 0.
Question 38 :
Find the roots of the quadratic equation (by using the quadratic formula): $\frac{1}{2}x^2-\sqrt{11}x+1=0$
Question 40 :
The product of Sunita’s age (in years) two years ago and her age four years from now is one more than twice her present age. What is her present age?
Question 41 :
Using method of completing the square , solve for x: $2x^2-5x+3=0$
Question 43 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Question 44 :
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
Question 45 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 – 7x + 3 = 0$
Question 47 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$
Question 48 :
Find the roots of the quadratic equation (by using the quadratic formula): $-3x^2+5x+12=0$
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 :
State True or False: Every quadratic equation has at least one real root.
