Question

for what value of a is -4a zero of the polynomial p(x) = x2-x-(2a+2)​

Answer 1

Answer:

p(x) = x² - x - (2a + 2)

If -4a is a zero of the polynomial then p(x) = 0

0 = (-4a)² - (-4a) - (2a + 2)

0 = 16a² + 4a - 2a - 2

0 = 16a² + 2a - 2

0 = 2(8a² + a - 1)

8a² + a - 1 = 0

Hope it helps u...

Answer 2

Answer:

$p(x) = {x}^{2} - x - (2a + 2) \\ \\ \rightarrow \: p( - 4a) = {( - 4a)}^{2} - ( - 4a) - (2a + 2) = 0\\ \\ \rightarrow 16 {a}^{2} + 4a - 2a - 2 = 0\\ \\ \rightarrow \: 16 {a}^{2} + 2a - 2 = 0 \\ \\ \rightarrow \: 8 {a}^{2} + a - 1 = 0 \\ \\ \\ \\on \: solving \: this \: equation \: \: we \: get \\ \\ \\ \\ { \boxed{ a = \frac{ - 1 + \sqrt{17} }{16} }}\\ \\ \\ \boxed{a = \frac{ - 1 - \sqrt{17} }{16} }$