If a and b 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) Given the quadratic equation $2ax^2 + (2a + b)x + b = 0$,where $a 
e 0$.The discriminant $D$ is given by $D = B^2 - 4AC$.Substituting the coeffic

Vedclass · Accepted Answer

Rational

Vedclass · Answer

(A) Given the quadratic equation $2ax^2 + (2a + b)x + b = 0$,where $a 
e 0$.The discriminant $D$ is given by $D = B^2 - 4AC$.Substituting the coefficients $A = 2a$,$B = (2a + b)$,and $C = b$:$D = (2a + b)^2 - 4(2a)(b)$$D = 4a^2 + 4ab + b^2 - 8ab$$D = 4a^2 - 4ab + b^2$$D = (2a - b)^2$.Since $a$ and $b$ are integers,$(2a - b)^2$ 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 $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0, a \ne 0,$ will be

Similar Questions

What is the major product of the following reaction?

Let $f(x) = \frac{2\sin^2 x - 1}{\cos x} + \frac{\cos x(2\sin x + 1)}{1 + \sin x}$. Then find $\int e^x (f(x) + f'(x)) dx$ (where $c$ is the constant of integration).

Two identical metal plates show the photoelectric effect when light of wavelength ${\lambda _A}$ falls on plate $A$ and ${\lambda _B}$ falls on plate $B$,where ${\lambda _A} = 2{\lambda _B}$. The maximum kinetic energy is:

Electric field at a point varies as $r^0$ for

Which orbital is dumb-bell shaped?

Vedclass Test Series

Exam Paper Generator

Online Exam Module