If one root of the equation x^2 + px + q = 0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the roots of the given equation $x^2 + px + q = 0$ be $\alpha$ and $\alpha^2$.From the relation between roots and coefficients,we have:$\alpha

Vedclass · Accepted Answer

$p^3 + q^2 + q(1 - 3p) = 0$

Vedclass · Answer

(D) Let the roots of the given equation $x^2 + px + q = 0$ be $\alpha$ and $\alpha^2$.From the relation between roots and coefficients,we have:$\alpha \cdot \alpha^2 = \alpha^3 = q$$\alpha + \alpha^2 = -p$Cubing both sides of the second equation:$(\alpha + \alpha^2)^3 = (-p)^3$$\alpha^3 + (\alpha^2)^3 + 3\alpha \cdot \alpha^2(\alpha + \alpha^2) = -p^3$Substitute $\alpha^3 = q$ and $\alpha + \alpha^2 = -p$ into the equation:$q + q^2 + 3q(-p) = -p^3$$p^3 + q^2 + q - 3pq = 0$$p^3 + q^2 + q(1 - 3p) = 0$.

If one root of the equation $x^2 + px + q = 0$ is the square of the other,then

Similar Questions

For the equation $ax^2 + bx + c = 0$,if $\alpha$ and $\beta$ are its roots,then the equation whose roots are $\alpha + \frac{1}{\beta}$ and $\beta + \frac{1}{\alpha}$ is:

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+bx-c=0$,then

If $\alpha, \beta, \gamma$ are roots of $x^3-5x+4=0$,then $(\alpha^3+\beta^3+\gamma^3)^2$ is equal to

If one real root of the quadratic equation $81x^2 + kx + 256 = 0$ is the cube of the other root,then a value of $k$ is

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module