Question

Find the value of p for which the quadratic equation 2x² - 6x + p = 0 has real and distinct roots.

Answer 1

For having distinct real roots,

Discriminant, D = b²−4ac>0

⇒(−6)²>4⋅2⋅p

⇒36>8p

⇒8p<36

⇒p<9/2

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Answer 2

D = b² -4ac > 0

⇒ (-6)² - 4 x 2 x p > 0

⇒ 36 - 8p > 0

⇒ 8p < 36

⇒ p < 36/8 

⇒ p < 9/2

Hence any value of p less than 9/2 gives the real and distinct roots of quadratic equation 2x² - 6x + p = 0