If a and b are odd integers, then the roots o | vedclass

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

Question

(A) The given quadratic equation is $2ax^2 + (2a + b)x + b = 0$. The discriminant $D$ is given by $D = B^2 - 4AC$. Here, $A = 2a$, $B = (2a + b)$, and

Vedclass · Accepted Answer

rational

Vedclass · Answer

(A) The given quadratic equation is $2ax^2 + (2a + b)x + b = 0$. The discriminant $D$ is given by $D = B^2 - 4AC$. Here, $A = 2a$, $B = (2a + b)$, and $C = b$. $D = (2a + b)^2 - 4(2a)(b) = 4a^2 + 4ab + b^2 - 8ab = 4a^2 - 4ab + b^2 = (2a - b)^2$. Since $a$ and $b$ are integers, $(2a - b)^2$ is a perfect square. If the discriminant of a quadratic equation with rational coefficients is a perfect square, the roots are rational. Thus, the roots are rational.

If $a$ and $b$ are odd integers, then the roots of the equation $2ax^2 + (2a + b)x + b = 0$, where $a \neq 0$, are

Similar Questions

If the roots of the equation $(a^2 + b^2)x^2 - 2b(a + c)x + (b^2 + c^2) = 0$ are equal,then in which progression are $a, b, c$?

If the bi-quadratic equation $f(x)=x^4+2x^3-16x^2-22x+7=0$ has $2+\sqrt{3}$ as one of its roots,then which of the following is not a root of $f(x)$?

Consider the equation $(1+a+b)^2=3(1+a^2+b^2)$ where $a, b$ are real numbers. Then,

Let $E$ denote the set of all integers $a$ such that the point of intersection of the parabola $y = x^2 + 2ax + 2021$ with the $x$-axis has rational coordinates. The largest element of $E$ is

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module