Question

Lep.9 € {12,3,4). The number of equations of the
(a) 15
(c) 8
(b) 9
(d) None of these
(1+ a + a?)(1+B+B?) is equal to
(a) zero
(c) negative
(b) positive
11. If a and Bare the roots of the equation ax + bx + C =0(a #0, a, b, c being different), then​

Answer 1

Answer:

1)15

2)positive

3)The given quadratic equation is ax  

2

+bx+c=0

⇒  Let two roots be α and β.

⇒  α=−β                     [ Given ]

⇒  α+β−  

a

−b

​  

 

⇒  −β+β=  

a

−−b

​  

 

⇒  0=  

a

−b

​  

 

∴  b=0                            ------- ( 1 )

We have one root negative so,

∴  αβ<0

∴    

a

c

​  

<0

So, here either c or a will be negative.

Means, a and c  will be having opposite sign.  

a>0,c<0 or c>0,a<0 and b=0.

In options we can see option C satisfy all the conditions.

∴  Posibble conditions are a>0,b=0,c<0

Step-by-step explanation: