Question

The roots of ax^2+x+1=0 , where A not equal to zero , are in the ratio 1 : 1. Then a is equal to :

Answer 1

Answer:

Here, ax^2+x+1=0 ; a not equal to 0

as we know relation b/w coefficient of quadratic eq. and their zeroes are

alpha + beta = -b/a ,

& alpha × beta=c/a.

as ratio of zeroes is 1:1 means both zeroes of given quad. eq. are equal.

i.e., alpha=beta

now from eq. coefficient we get

a=a , b=1& c=1 .

clearly, we have

2alpha=-1/a -(1)& (alpha)^2 =1/a-(2)

adding (1)&(2) we get ,

(alpha)^2 +2alpha= 0

i.e. alpha (alpha+2)=0

i.e. alpha=0 or alpha=-2

but ,alpha=0 is not possible.

thus, alpha=-2

putting the value of alpha in (1) we get:

a=1/4 ans.

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