Step-by-step explanation:
We have,
[tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]
To find, the value of h = ?
∴ [tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]
⇒ [tex]6h^5[/tex] + (0)[tex]h^4[/tex] - 12[tex]h^3[/tex] + (0)[tex]h^3[/tex] + (0)h = 0
⇒ [tex]6h^5[/tex] + 0 - 12[tex]h^3[/tex] + 0 + 0 = 0
⇒ [tex]6h^5[/tex] - 12[tex]h^3[/tex] = 0
Taking 6 [tex]h^3[/tex] as common, we get
[tex]6h^3(h^2-2)[/tex] = 0
⇒6[tex]h^3[/tex] = 0 or, [tex]h^2[/tex] - 2 = 0
⇒ 6[tex]h^3[/tex] = 0 ⇒ h = 0
⇒ [tex]h^2[/tex] = 2
⇒ h = ± [tex]\sqrt{2}[/tex]
Hence, the value of h = 0, ± [tex]\sqrt{2}[/tex]
