Question 1 :
Justify why the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$
Question 2 :
Find the roots of the following quadratic equation (by the factorisation method): $\frac{2}{5}x^2-x-\frac{3}{5}=0$
Question 4 :
Find the nature of the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$
Question 5 :
Find the roots of the quadratic equation (by using the quadratic formula): $-3x^2+5x+12=0$
Question 6 :
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 7 :
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 8 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 9 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$
Question 10 :
What is the general expression (standard form) for quadratic equations ?
Question 11 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$
Question 12 :
Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?
Question 13 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 15 :
Represent the following situation in the form of a quadratic equation : Rohan’s mofher is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 16 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x – 4 = 0$
Question 17 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$
Question 19 :
Justify why the following quadratic equation has two distinct real roots: $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$
Question 20 :
Find the positive root of the equation $2x^2 + x - 300 = 0$, by factorisation.
Question 21 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.
Question 22 :
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 23 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$
Question 25 :
Find the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$.
Question 26 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$
Question 27 :
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?
Question 28 :
What are the roots of $6x^2-\sqrt{2}x-2=0$ (by the factorisation of the corresponding quadratic polynomial)?
Question 29 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2+x-1=0$
Question 30 :
Represent the following situation in the form of quadratic equations: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 31 : <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 33 :
Represent the following situation in the form of quadratic equations: The product of two consecutive positive integers is 306. We need to find the integers.
Question 34 :
Which constant should be added and subtracted to solve the quadratic equation $4x^2-\sqrt{3}x-5=0$ by the method of completing the square?
Question 35 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$
Question 36 :
Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Question 37 :
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 38 : <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 39 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2+2\sqrt{2}x-6=0$
Question 41 :
Find the roots of the quadratic equation (by using the quadratic formula): $2x^2-3x-5=0$
Question 42 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$
Question 43 :
Using method of completing the square , $x^2+4x$ can be written as ?
Question 44 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?
Question 45 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+4\right)^2-8x=0$
Question 46 :
Find the roots of the quadratic equation (by using the quadratic formula): $-x^2+7x-10=0$
Question 47 :
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 48 :
What are the roots of the quadratic equation $2x^2-\sqrt{5}x-2=0$ using the quadratic formula.
Question 49 :
State True or False whether the following quadratic equation has two distinct real roots: $x\left(1-x\right)-2=0$
