If p and q are odd integers,then the roots of | vedclass

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

Question

(A) The given quadratic equation is $2px^{2} + (2p + q)x + q = 0$.The discriminant $D$ is given by $D = b^{2} - 4ac$.Substituting the coefficients $a

Vedclass · Accepted Answer

rational

Vedclass · Answer

(A) The given quadratic equation is $2px^{2} + (2p + q)x + q = 0$.The discriminant $D$ is given by $D = b^{2} - 4ac$.Substituting the coefficients $a = 2p$,$b = (2p + q)$,and $c = q$:$D = (2p + q)^{2} - 4(2p)(q)$$D = 4p^{2} + q^{2} + 4pq - 8pq$$D = 4p^{2} + q^{2} - 4pq$$D = (2p - q)^{2}$Since $p$ and $q$ are integers,$D$ is a perfect square of an integer.For a quadratic equation with rational coefficients,if the discriminant is a perfect square,the roots are rational.

If $p$ and $q$ are odd integers,then the roots of the equation $2px^{2} + (2p + q)x + q = 0$ are

Similar Questions

The minimum value of $f(x) = x^2 + 4x + 5$ is . . . . . . ,where $x \in R$.

If the equation $x^4+ax^3+bx^2+cx+d=0$ has three equal roots,then that root is

Let $f: R \rightarrow R$ be the function $f(x) = (x - a_1)(x - a_2) + (x - a_2)(x - a_3) + (x - a_3)(x - a_1)$ with $a_1, a_2, a_3 \in R$. Then,$f(x) \geq 0$ if and only if

If all roots of the equation $x^3 - 2ax^2 + 3bx - 8 = 0$ are positive,where $a, b \in R$,then the minimum value of $b$ is:

If $\alpha$ is a root of multiplicity $3$ of the equation $x^5-8x^4+25x^3-38x^2+28x-8=0$,then $\alpha^2-5\alpha+6=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module