Question

in the following determine the set of values of p for which the given quadratic equation has real roots X² + 2x + p = 0​

Answer 1

Answer:

Hey mate,

here is your answer

The given quadratic equation is,

2x2+3x−p=0

Here,

a=2, b=3, c=−p

If the equation is supposed to have real roots, then D≥0. Therefore,

b2−4ac≥0

9−4×2×(−p)≥0

9+8p≥0

p≤89​

Thus, the values of p for which the equation has real roots are (−∞,8/9​]

Answer 2

Answer:

real roots, D≥0

b

2

−4ac≥0

In the given equation, a=P, b=4 and c=1

b

2

−4ac=(4

2

)−4P×1≥0

16−4P≥0

4P≤16

P≤4