Please can someone help me show that the roots of this equation is real

If the roots of the equation px^2 +qx +r =0 are real, show that the roots of the equation
r^2x^2 + (2pr-q^2)x + p^2 = 0 are also real

Since the roots of the equation px^2 +qx +r =0 are real,
discriminant = q^2 - 4qr ≥ 0

For r^2x^2 + (2pr-q^2)x + p^2 = 0,
discriminant
= (2pr-q^2)^2 - 4r^2*p^2
= (2pr-q^2+2pr)(2pr-q^2-2pr)
= (4pr-q^2)(-q^2)
= q^2(q^2-4pr) ≥ 0, since q^2 - 4qr ≥ 0 and q^2 ≥ 0
So, the roots of the equation r^2x^2 + (2pr-q^2)x + p^2 = 0 are also real.

r^2x^2 + (2pr-q^2)x + p^2 = 0
take a=r^2, b=(2pr-q^2), c=p^2
Now if b^2>=4ac, the roots will be real.

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