Question

The equation whose roots are the squares of the roots of the equation ax2 + bx + c = 0 is​

Answer 1

Step-by-step explanation:

Let α,β be the roots of the given quadratic equation

ax

2

+bx+c=0

α+β=−

a

b

αβ=

a

c

Now, sum of roots =α

2

+β

2

=(α+β)

2

−2αβ

=

a

2

b

2

−2ac

Product of roots =α

2

β

2

=

a

2

c

2

Required quadratic equation is

x

2

−

a

2

b

2

−2ac

x+

a

2

c

2

=0

⇒a

2

x

2

−(b

2

−2ac)x+c

2

=0