Test Details

Quadratic Equations

Feb 17, 8:30 PM

60 minutes

Feb 17, 9:30 PM

50.0 marks

MCQ

25 questions

Sheeja N

P. G, B.Ed in Maths

Class Details

English

Mathematics

Class 10

English

Mathematics

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Question Text

Question 1 :
For the expression $ax^2 + 7x + 2$ to be quadratic, the necessary condition is

Question 2 :
Check whether the given equation is a quadratic equation or not. $3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$

Question 3 :
If $x - 4$ is one of the factor of $x^{2} - kx + 2k$, where $k$ is a constant, then the value of $k$ is

Question 4 :
The following equation is a qudratic equation. $16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$

Question 7 :
If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$, and $-1$ is a root of $f(x) = 0$, then the other root of $f(x) = 0$ is :

Question 10 :
Check whether the following is a quadratic equation.$(x - 3) (2x + 1) = x (x + 5)$

Question 11 :
Which of the following equations has no solution for $a$ ?

Question 12 :
If difference of roots of the equation$\displaystyle x^{2}+px+8= 0$ is $2$, then $p$ is equal to

Question 13 :
If a, b, c $\epsilon\ Q\ $, then the roots of the equation $(b + c - 2a) x^{2} + (c+a-2b) x+ (a+b-2c) = 0$ are

Question 15 :
If the roots of the equation $\displaystyle \left ( a^{2}+b^{2} \right )x^{2}-2b\left ( a+c \right )x+\left ( b^{2}+c^{2} \right )=0 $ are equal then

Question 16 :
Find the discriminant of the equation and the nature of roots. Also find the roots.$2x^2 + 5 \sqrt 3x + 6 =0$

Question 17 :
Assertion: If $a$ and $b$ are integers and the roots of $x^2+ax+b=0$ are rational then they must be integers. Reason: If the coefficient of $x^2$ in a quadratic equation is unity then its roots must be integers.

Question 18 :
Find the values of $k$ for the following quadratic equation, so that they have two real and equal roots:$4x^2 - 2(k + 1)x + (k + 4) = 0$

Question 19 :
Assertion (A): The roots of $(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$  are real Reason (R): A quadratic equation with non-negative discriminant has real roots .

Question 20 :
If in applying the quardratic formula to a quadratic equation $f(x) = ax^2 + bx + c = 0$, it happens that $c = b^2/4a$, then the graph of $y = f(x)$ will certainly:

Question 22 :
Given expression is $x^{2} - 3xb + 5 = 0$. If $x = 1$ is a solution, what is $b$?

Question 24 :
If one of the roots of $x^2-bx+c=0,\:(b,c)\:\epsilon\:Q$ is $\sqrt{7-4\sqrt 3}$ then:

Question 25 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$. Then the roots of the correct equation are

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