Answer-I. p2 + 2p – 8 = 0 &...

Q: Answer-I. p2 + 2p &ndash; 8 = 0 &...

I. p2 2p ndash 8 0 rArr p 4 p ndash 2 0 rArr p 2, - 4 II. q2 ndash 5q 6 0 rArr q - 3 q - 2 0 rArr q 2, 3 Hence, q ge 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 ge p.

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Question

I. p2 + 2p – 8 = 0
II. q2 – 5q + 6 = 0

A if p = q Correct Incorrect

B if p > q Correct Incorrect

C if q > p Correct Incorrect

D if p ≥ q Correct Incorrect

E if q ≥ p Correct Incorrect

Detailed Solution

I. p²+ 2p – 8 = 0

⇒ (p + 4) ( p – 2) = 0

⇒ p = 2, - 4

II. q² – 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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I. p2 + 2p – 8 = 0II. q2 – 5q + 6 = 0