Find **Solved Practice Paper for IIT JEE Main** in this article. This practice paper consists of 10 questions. These questions are from the chapter Theory of Equations of Mathematics. We have tried to include all important concepts in these questions. Also, detailed solution of each question has been provided. All questions are very important from examination point of view.

These questions are based on roots of quadratic equations, real and imaginary roots, number of roots in an interval etc.

**Note:**

If the sum of all the coefficients of a quadratic equation is zero, then roots of the equation are 1 and C/A, where C is constant and A is the coefficient of *x*^{2}_{.}

**Q1.** If *a,* *b,* *c* are distinct numbers in arithmetic progression, then both the roots of the quadratic equation

(*a* + 2*b *-* *3*c*)*x*^{2}* + *(*b* + 2*c* - 3*a*)*x* + (*c* + 2*a* - 3*b*) = 0 are

(a) real

(b) positive

(c) negative

(d) rational

**Correct Option: (b)**

**Sol. **

Let *A* = *a* + 2*b* – 3*c*, *B* = *b* + 2*c* – 3*a*, *C* = *c* + 2*a* – 3*b*

Now,

*A* + *B* + *C *= *a* + 2*b* – 3*c+ b* + 2*c* – 3*a+ c* + 2*a* – 3*b=*0

**Correct Option: (a)**

**Sol.**

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**Sol.**

**Correct Option: (d)**

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