Answer:
p = 0 , p = ± [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
4[tex]p^{4}[/tex] - 25p² = - 16p² ( add 16p² to both sides )
4[tex]p^{4}[/tex] - 9p² = 0 ← factor out p² from both sides
p²(4p² - 9) = 0 ← factor is a difference of squares
p²(2p - 3)(2p + 3) = 0
Equate each factor to zero and solve for p
p² = 0
p = 0 ( multiplicity of 2 )
2p - 3 = 0 ⇒ 2p = 3 ⇒ p = [tex]\frac{3}{2}[/tex]
2p + 3 = 0 ⇒ 2p⇒ = - 3 ⇒ p = - [tex]\frac{3}{2}[/tex]
