Question

Find value of a for which one root of equation (a^2+ a + 1)x^2 + (a - 1)x+ a^2 = 0 is greater than 3 and other is smaller than 3. ​

Answer 1

Answer:

Step-by-step explanation:

x2−(a+1)x+a2+a−8=0  

Since roots are different, therefore D>0

⇒(a+1)2−4(a2+a−8)>0

⇒(a−3)(3a+l)<0

There are two cases arises.

Case I. a−3>0 and 3a+1<0

⇒a>3 and a<−113

Hence, no solution in this case

Case II : a−3<0 and 3a+11>0

⇒a<3 and a>−113

∴−113<a<3⇒−2<a<3