Question

If p and q are the roots of the equation x^2 + b/a x + c/a = 0.
What is p^2 + q^2 ?

Answer 1

Answer:

Step-by-step explanation:

Consider the quadratic equation :

ax2+bx+c=0

having roots p and q

⟹p+q=−ba …. (1)

and pq=ca ….(2)

Now we need to find the quadratic equation whose roots are p2 and q2

Sum of roots :

using (1) and (2)

p2+q2=(p+q)2−2pq=(−ba)2−2ca ….(3)

Product of roots:

using (2)

p2q2=(pq)2=(ca)2 …. (4)

So, the required quadratic equation will be:

x2−(sum of roots)x+product of roots=0

Substitute the values from (3) and (4)

x2−(b2a2−2ca)x+(ca)2=0

⟹a2x2−(b2−2ac)x+c2=0