Verified answer

Explicação passo-a-passo:

delta>0

b²-4ac>0

(-6)²-4.3/2.2p>0

36-24/2P>0

36-12P>0

-12p>-36 x(-1)

12P>36

P>36/12

P>3

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\mathsf{\dfrac{3}{2}\:x^2- 6x + 2p = 0}\rightarrow\begin{cases}\mathsf{a = 3/2}\\\mathsf{b = -6}\\\mathsf{c = 2p}\end{cases}[/tex]

[tex]\boxed{\boxed{\mathsf{\Delta > 0}}}\rightarrow\textsf{duas ra{\'i}zes reais e distintas.}[/tex]

[tex]\mathsf{b^2 - 4.a.c > 0}[/tex]

[tex]\mathsf{(-6)^2 - 4.\left(\dfrac{3}{\not2}\right).(\not2p) > 0}[/tex]

[tex]\mathsf{36 - 12p > 0}[/tex]

[tex]\mathsf{-12p > -36}[/tex]

[tex]\mathsf{12p < 36}[/tex]

[tex]\mathsf{p < \dfrac{36}{12}}[/tex]

[tex]\boxed{\boxed{\mathsf{p < 3}}}[/tex]