Test Details

Quadratic Equations

Jan 20, 11:10 AM

50 minutes

Jan 20, 12:00 PM

50.0 marks

MCQ

25 questions

RK SIR

मैं पिछले 5 सालों से गणित और साइंस छात्र छात्राओं को पढ़ा रहा हूं मेरे पढ़ाने से काफी छात्र अच्छे मार्क्स से पास होते जा रहे हैं अतः आप मेरे क्लास को ज्वाइन करें

Class Details

Mathematics

Class10

Mathematics

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Question Text

Question 1 :
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 2 :
Find the roots of the following quadratic equation (by the factorisation method): $3\sqrt{2}x^2-5x-\sqrt{2}=0$

Question 3 :
A quadratic equation $ax^2 + bx + c =0$ has no real roots when :

Question 4 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf5273b230584979a4d.jpg' /> Find the dimensions of the prayer hall given in the above figure.

Question 5 :
Check whether the following is quadratic equation : $(x+1)^2 = 2(x-3)$

Question 9 :
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 10 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$

Question 11 :
Check whether the following is a quadratic equation: $x^2 – 2x = (–2) (3 – x)$

Question 13 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$

Question 14 :
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 15 :
Represent the following situation in the form of a quadratic equation : A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h lesss, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Question 16 :
State true or false: $b^2 – 4ac$ is called the discriminant of the quadratic equation $ax^2 + bx + c = 0$.

Question 17 :
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 18 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$

Question 20 :
Justify why the following quadratic equation has no two distinct real roots: $\left(x+4\right)^2-8x=0$

Question 21 :
State True or False whether the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$

Question 22 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$

Question 23 :
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 25 :
Check whether the following is a quadratic equation: $(x – 2)(x + 1) = (x – 1)(x + 3)$

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