Quadratic Equations Set-1

Q1. The sum of all real values of $k$ for which the quadratic

has equal roots is:

Q2. If the two real roots of a quadratic differ by $3$ and their sum is $5$, the monic quadratic equation having these roots is:

Q3. For how many real values of $k$ does the equation

have equal roots (consider only values of $k$ for which the equation is quadratic)?

Q4. For which real values of $m$ do both roots of

remain positive?

Q5. If the roots of the quadratic $ax^2+bx+c=0$ (with $a\neq0$) are real and one root is twice the other, then the ratio $b^2:ac$ equals:

Q6. For the quadratic $x^2 - 5x + p = 0$, the difference between its roots is $3$. Find $p$.

Q7. For which values of $k$ does the quadratic $kx^2+(k-3)x+1=0$ have two real and positive roots?

Q8. One root of the quadratic $x^2-(t+3)x+(t+2)=0$ is twice the other. The possible values of $t$ are

Q9. For which integer values of $k$ does the quadratic $x^2+(k-1)x+(k+1)=0$ have at least one integer root?

Q10. Find all real $m$ for which the equation $(m^2+m-2)x^2+2(m-1)x+1=0$ has equal real roots.

Q11. If one root of the quadratic $x^2-(k+1)x+k=0$ is twice the other, the possible values of $k$ are:

Q12. For which values of $p$ does the quadratic $x^2+(p-3)x+(p+1)=0$ have roots whose difference is $2$?

Q13. If the roots of $x^2+(k+1)x+k=0$ differ by $1$, then $k=$

Q14. For which values of $k$ do both roots of $x^2-4x+k=0$ lie strictly inside the interval $(1,3)$?

Q15. Let $\alpha,\beta$ be the roots of $x^2-Sx+P=0$. If $\alpha+\beta=4$ and $\alpha^3+\beta^3=52$, then $P=$