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Question
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
Options
p < `(9)/(2)`
p ≤ `(9)/(2)`
p > `(9)/(2)`
p ≥ `(9)/(2)`
Solution
2x² – 6x + p = 0
Here, a = 2, b = –6, c = p
b2 – 4ac
= (–6)2 – 4 x 2 x p
= 36 – 8p
∵ Roots are real and unequal.
∴ b2 – 4ac > 0
⇒ 36 – 8p > 0
⇒ 36 > 8p
⇒ `(36)/(8)` > p
⇒ p < `(36)/(8)`
⇒ p < `(9)/(2)`.
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