Question

2. If the sum of the roots of the quadratic equation
ax 2 + bx + c = 0 is equal to the sum of the squares of their
reciprocals, then a/c,bla,c/b are in.​

Answer 1

Answer:

2

Step-by-step explanation:

Let P and Q are roots of equations

So, P+Q=-b/a

PQ=c/a

According to the question ,

P+Q=1/p^2+1/q^2

-b/a={(p + q)^2-2pq}/P^2Q^2

-b/a=(b^2/a^2-2c/a)/(c/a)^2

-b*c^2/a^3=b^2/ a^2 -2c/a

2c/a=b^2/ a^2bc^2/a^3=b(ab+c^2)/a^3

2ca^2=b^2a+bc^2

2=b^2a/a^2c+bc^2+a^2c

=b^2/ac +bc/a^2=2(answer)