Question

for what value of p the quadratic equation 2x^2-6x+p=0has real and distinct roots​

Answer 1

I take the equation

2x² + 6x + p = 0

Comparing this equation with the standard quadratic equation

ax² + bx + c = 0,

a = 2, b = 6, c = p .

Since the two roots are real and distinct (unequal),

b² - 4ac is positive (>0)

Substituting the values for a, b and c from above,

6² - 4 x 2 x p > 0

Or, 36 - 8p > 0

Dividing both sides by 4,

4.9/4 - 8p/4 > 0

Or, 9 - 2p > 0

Or, 9 > 2p

Or, 2p < 9

Dividing both sides by 2,

p < 9/2 or 4.5 (Proved)

Answer 2

Answer: p is less than 9/2 or 4.5

Step-by-step explanation: I take the equation

2x² + 6x + p = 0

Comparing this equation with the standard quadratic equation

ax² + bx + c = 0,

a = 2, b = 6, c = p .

Since the two roots are real and distinct (unequal),

b² - 4ac is positive (>0)

Substituting the values for a, b and c from above,

6² - 4 x 2 x p > 0

Or, 36 - 8p > 0

Dividing both sides by 4,

4.9/4 - 8p/4 > 0

Or, 9 - 2p > 0

Or, 9 > 2p

Or, 2p < 9

Dividing both sides by 2,

p < 9/2 or 4.5 (Proved)