Quadratic Function

Question

The quadratic equation x(p-x)=x+4 has no real roots. Find the range of values of p.

How to do this step by step

Answer: -3<p<5

Answer 1

Get the equation in the standard form of a quadratic equation, and make the discriminant negative.

x(p - x) = x + 4

xp - x² = x + 4

-x² + (p - 1)x - 4 = 0

x² + (1 - p) + 4 = 0

D = (1 - p)² - 4(4) = (1 - p)² - 16 = 0

(1 - p)² = 16

1 - p = 4 or -4

If 4, then

p = -3

If -4, then

p = 5

Then p must be between -3 and 5.

-3 < p < 5