Question

find zeros of xcube-5xsquare -16+80​

Answer 1

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• The zeros of the given cubic equation are 5, 4 and -4.

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given:

→ x³ - 5x² - 16x + 80 = 0

→ x²(x - 5) - 16x + 80 = 0    [Taking x² as common.]

→ x²(x - 5) - 16(x - 5) = 0     [Taking -16 as common.]

→ (x² - 16)(x - 5) = 0             [Taking (x - 5) as common.]

→ (x² - 4²)(x - 5) = 0

→ (x + 4)(x - 4)(x - 5) = 0     [Using identity a² - b² = (a + b)(a - b)]

→ (x + 4) = 0 or (x - 4) = 0 or (x - 5) = 0

→ x = 5, 4, -4

⊕ So, the roots of the given equation are 5, 4 and -4.