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True/False

Mathematics

Chapter 4: Quadratic Equations

Class 10

True False Mathematics Chapter 4: Quadratic Equations for Class 10th is very important as these type of questions help in scoring good marks. True False type questions are to be answered to the point and hence very helpful in overall scoring. True False Type of questions helps students to think Critically on every aspects of life.

Here is a collection of few questions for CBSE Class 10th Term 2 Exams. These True False are fully solved. 

State whether the following statements are True/False.

Question.1.
If the product `ac` in the quadratic equation `ax^{2}+bx+c=0` is negative, then the equation cannot have non-real
roots.

True

Question.2.
If 2 is a zero of the quadratic polynomial `p(x)` then 2 is a root of the quadratic equation `p(x)=0`.

True

Question.3.
If sum of the roots is 2 and product is 5, then the quadratic equation is `x^{2}-2x+5=0`

True

Question.4.
A quadratic equation may have no real root.

True

Question.5.
The degree of a quadratic polynomial is atmost 2.

False

Question.6.
The roots of the equation `(x-3)^{2}=3` are `3\pm \sqrt{3}`.

True

Question.7.
Every quadratic equation has at least two roots.

False

Question.8.
`(x-2)(x+1)=(x-1)(x+3)` is a quadratic equation.

False

Question.9.
Every quadratic equation has at most two roots.

True

Question.10.
The equation `(x+2)^{2}=0` has real roots.

True

Question.11.
If we can factorise `ax^{2}+bx+c=0, a ≠ 0`, into a product of two linear factors, then the roots of the quadratic equation `ax^{2}+bx+c=0` can be found by equating each factor to zero.

True

Question.12.
`x^{2}+x-306=0` represent quadratic equation where product of two consecutive positive integer is 306.

True

Question.13.
If the coefficient of `x^{2}` and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

True

Question.14.
`(x^{2}+3x+1)=(x-2)^{2}` is not a quadratic equation.

True

Question.15.
A quadratic equation has its degree at least two.

False

Question.16.
0.2 is a root of the equation `x^{2}-0.4=0`.

False

Question.17.
If the value of discriminant is equal to zero, then the equation has real and distinct roots.

False

Question.18.
A quadratic equation cannot be solved by the method of completing the square.

False

Question.19.
Every quadratic equation has exactly one root.

False

Question.20.
For the expression `ax^{2}+7x+2=0` to be quadratic, the possible values of a are non-zero real numbers.

True

Question.21.
Every quadratic equation has at least one real root. 

False

Question.22.
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.

True

Question.23.
The nature of roots of equation `x^{2}+2x\sqrt{3}+3=0` are real and equal.

True

Question.24.
Sum of the reciprocals of the roots of the equation `x^{2}+px+q=0` is `\frac{1}{p}`.

False

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