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

विकल्प

• p < `(9)/(2)`

• p ≤ `(9)/(2)`

• p > `(9)/(2)`

• p ≥ `(9)/(2)`

Answer 1

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)`.