Quadratic Equations: JEE Main Mathematics Previous Year Questions

316 previous year questions from Quadratic Equations. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.If $\alpha \text{,}\beta$ are the roots of $x^2-x+1=0$, then the quadratic equation whose roots are ${\alpha }^{2015}\text{,}{\beta }^{2015}$ is
2. 2.The number of all possible positive integral values of α for which the roots of the quadratic equation, $6x^2$ – 11x + α = 0 are rational numbers is:
3. 3.If $\alpha \text{,}\beta \text{,}\gamma$ are the roots of the equation $4x^3+12x^2-7x+165=0$ and $\alpha +5\text{,}\beta +5\text{,}\gamma +5$ are the roots of…
4. 4.Let $S=\{\alpha \text{:}{\text{log}}_2(9^{2a-4}+13)-{\text{log}}_2\text{(}\frac{5}{2}.3^{2a-4}+1\text{)}=2\}$Then the maximum value of $\beta$ for whi…
5. 5.Let $\alpha \text{,}\beta$ be roots of $x^2+\sqrt{2}x-8=0$. If $U_n={\alpha }^n+{\beta }^n$, then $\frac{U_{10}+\sqrt{2}{U}_9}{2U_8}$ is equal to…
6. 6.A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B a…
7. 7.If $\alpha \text{,}\beta \text{,}\gamma$ are the roots of the equation $x^3-5x^2-2x+24=0$ then…
8. 8.If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^2+\text{αx}+\beta >0$, for all…
9. 9.The number of solutions of the equation $(\frac{9}{x}-\frac{9}{\sqrt{x}}+2)(\frac{2}{x}-\frac{7}{\sqrt{x}}+3)=0$ is:
10. 10.The integer $\text{’}k\text{’}$, for which the inequality $x^2-2\text{(}3k-1\text{)}x+8k^2-7>0$ is valid for every $x$ in $R$ is:
11. 11.The sum of all the real numbers satisfying the equation $x^2+\text{|}x-3\text{|}=4$ is
12. 12.Let $\alpha$be a root of the equation 1 + $x^2$ + $x^4$ = 0. Then the value of ${\alpha }^{1011}+{\alpha }^{2022}-{\alpha }^{3033}$ is equal to:
13. 13.If $a\text{,}b$ and $c$ are the roots of $x^3+\text{qx}+r=0$, then $\text{(}a-b{\text{)}}^2+\text{(}b-c{\text{)}}^2+\text{(}c-a{\text{)}}^2=$
14. 14.If $4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}$ then the value of $x$ is
15. 15.If $\alpha \text{,}\beta \text{,}\gamma$ are the roots of $f\text{(}x\text{)}=x^3-9x^2+26x-24$, then…
16. 16.If $x^2+2\text{px}-2p+8>0$ for all real values of $x$, then the set of all possible values of $p$ is
17. 17.If $f\text{(}x\text{)}=2x^3+m{x}^2-13x+n$ and 2,3 are the roots of the equation $f\text{(}x\text{)}=0$, then the values of $m$ and $n$ are
18. 18.If $\lambda$ be the ratio of the roots of the quadratic equation in $x\text{,}3m^2{x}^2+m(m-4)x+2=0$, then the least value of $m$ for which…
19. 19.If the value of real number $a>0$ for which $x^2-5\text{ax}+1=0$ and $x^2-\text{ax}-5=0$ have a common real roots is $\frac{3}{\sqrt{2\beta }}$ then $\beta$…
20. 20.If $\alpha \text{,}\beta$ are the irrational roots of the equation $3p^2{x}^3+p{x}^2+\text{qx}+3=0$ when $p=1$ and $q=-7$ then…
21. 21.If $x^2-3\text{ax}+14=0$ and $x^2+2\text{ax}-16=0$ have a common root, then $a^4+a^2$.
22. 22.The number of integer solutions of the equation $\text{|}1-i{\text{|}}^x=2^x$ is
23. 23.Let $\alpha$ and $\beta$ be the roots of $x^2-6x-2=0$, with $\alpha >\beta$. If $a_n={\alpha }^n-{\beta }^n$ for $n\ge 1$, then the value of…
24. 24.The sum of the complex roots of the equation $x^4-2x^3+x-380=0$ is
25. 25.The minimum value of the sum of the squares of the roots of $x^2$ + (3 - a)x + 1 = 2a is: