I. p^{2}+ 2p – 8 = 0 II. q^{2} – 5q + 6 = 0

I. p^{2}+ 2p – 8 = 0

⇒ (p + 4) ( p – 2) = 0

⇒ p = 2, - 4

II. q^{2}– 5q + 6 = 0

⇒ ( q - 3) ( q - 2) = 0

⇒ q = 2, 3

Hence, q ≥ p

Alternate Method:

if signs of quadratic equation is +ve and -ve respectively then the roots of equation will be +ve and -ve. (note: -ve sign will come in larger root)

So, roots of first equation = p = 2, -4

if signs of quadratic equation is -ve and +ve respectively then the roots of equation will be +ve and +ve.

So, roots of second equation = q = 2, 3

After comparing roots of quadratic eqution we can conclude that q ≥ p.

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