Test Details

Quadratic Equations

Chapter wise test

Feb 25, 7:30 PM

60 minutes

Feb 25, 8:30 PM

80.0 marks

MCQ

40 questions

Suraj Sagar

I'm a professional teacher. Guiding and coaching students from 12 years. I'm a meditator also. I prepare students not only with subjects also guiding them to achieve their goals. I trust in hard work. Part of Ed-tech Platform serving WORK FROM ANYWHERE Spend daily 2hrs Learn get trained And Earn 2k to 5k daily

Class Details

Science

English Language

Spoken English

Maths

Literature

Meditation

Right Way

Science

English Language

Spoken English

Maths

Literature

Meditation

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Question Text

Question 1 :
State True or False whether the following quadratic equation has two distinct real roots: $x^2-3x+4=0$

Question 2 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $4x^2+4\sqrt{3}x+3=0$

Question 5 :
Justify why the following quadratic equation has no two distinct real roots: $\left(x+4\right)^2-8x=0$

Question 7 :
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 8 :
Using method of completing the square , $9x^2-15x+6=0$ can be written as ?

Question 9 :
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

Question 10 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.

Question 11 :
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Question 12 :
State True or False: Every quadratic equation has exactly one root.

Question 15 :
What are the roots of the quadratic equation $2x^2-\sqrt{5}x-2=0$ using the quadratic formula.

Question 16 :
Check whether the following is a quadratic equation: $(x + 2)^3 = x^3 – 4$

Question 17 :
State True or False: Every quadratic equation has at least one real root.

Question 18 :
Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x+2=0$, by factorisation.

Question 19 :
Justify why the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$

Question 20 :
State True or False: A real number α is said to be a root of the quadratic equation a$x^2$ + bx + c = 0, if a$α^2$ + bα + c = 0.

Question 21 :
Check whether the following is a quadratic equation: $x(2x + 3) = x^2 + 1$

Question 22 :
Justify why the following quadratic equation has no two distinct real roots: $2x^2-6x+\frac{9}{2}=0$

Question 23 :
Check whether the following is a quadratic equation: $x^2 + 3x + 1 = (x – 2)^2$

Question 24 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$

Question 25 :
A quadratic equation $ax^2 + bx + c =0$ has two equal real roots when :

Question 26 :
Does the following equation has the sum of its roots as 3? $2x^2-3x+6=0$

Question 27 :
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 28 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$

Question 29 :
Find the roots of the quadratic equation (by using the quadratic formula): $2x^2-3x-5=0$

Question 30 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2-6x+\frac{9}{2}=0$

Question 31 :
State true or false: $b^2 – 4ac$ is called the discriminant of the quadratic equation $ax^2 + bx + c = 0$.

Question 32 :
Using method of completing the square , solve for x: $5x^2-6x-2=0$

Question 33 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.

Question 34 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $kx (x – 2) + 6 = 0$

Question 35 :
Using method of completing the square , solve for x: $4x^2+3x+5=0$

Question 36 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$

Question 38 :
Check whether the following is quadratic equation : (x - 2)(x +1)=(x - 1)(x + 3)

Question 39 :
Check whether the following is a quadratic equation: $(x – 2)^2 + 1 = 2x – 3$

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