p > [tex]\frac{2}{3}[/tex]
given a quadratic equation in standard form : ax² + bx + c = 0 : a ≠ 0
We can determine the nature of the roots using the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 , then 2 real and distinct roots
• If b² - 4ac = 0, then 2 real and equal roots
• If b² - 4ac < 0, then no real roots
px² + 4x + 6 = 0 is in standard form
with a = p, b = 4 and c = 6
For no real solution, solve b² - 4ac < 0
4² - (4 × p × 6 ) < 0
16 - 24p < 0 ( subtract 16 from both sides )
- 24p < - 16 ( divide both sides by - 16 , reversing the symbol in doing so )
p > [tex]\frac{16}{24}[/tex]
Thus for the equation to have no real solutions p > [tex]\frac{2}{3}[/tex]
