Question

The equation (a + 2)x^2 +( a -3)x= 2a - 1, a=-2 has roots rational for

Answer 1

The equation (a + 2)x^2 +( a -3)x= 2a - 1, a=-2 has roots rational for

f(x) =  (a + 2)x^2 +( a -3)x - (2a - 1)

(a + 2)x^2 +( a -3)x - (2a - 1) = 0

solving this quadratic equation, we get,

x = 1

$x=\dfrac{-2a+1}{a+2}$ for a ≠ -2

for a = -2, the function becomes indefinable.

Therefore, The roots of the equation f(x) = 0 area rational if a is a rational and not equal to 2.

Answer 2

In the equation (a+2)x^2+(a-3)x=2a-1, a=-2 has roots rational for

Stepwise explanation is given below:

- It is said that the equation has roots,

f(x) = (a+2)x^2+(a-3)x-(2a-1)

(a+2)x^2+(a-3)x-(2a-1) = 0

- As the value of a is given that is a= -2

- By using the value of a in the equation f(x).

(-2+2)x^2 +(-2-3)x -(2*-2-1) = 0

0+(-5) x-(-5) = 0

-5x +5= 0

x = -5/-5

x = 1

x=1

x= (-2a+1)/(a+2)

- For a is not equal to -2

For a=-2, the function becomes indefinable.

- So, the roots of the equation f(x)=0 area rational and not equal to 2.