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 nonreal
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 `(x3)^{2}=3` are `3\pm \sqrt{3}`.
True
Question.7.
Every quadratic equation has at least two roots.
False
Question.8.
`(x2)(x+1)=(x1)(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}+x306=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)=(x2)^{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 nonzero 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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