Question

If 2 and 4 are zeroes of the polynomial f(x) = x2 + ax – 8, then find the value of a​

Answer 1

Step-by-step explanation:

$\bull \bf \: f(x) = {x}^{2} + ax - 8 \\ \\ \tt \twoheadrightarrow \: f(2) = {2}^{2} + a(2) - 8 \\ \\ \tt \twoheadrightarrow \: 4 + 2a - 8 \\ \\ \tt \twoheadrightarrow \: 2a - 4 \dots(1) \\ \\ \tt \twoheadrightarrow \: f(4) = {4}^{2} + a(4) - 8 \\ \\ \tt \twoheadrightarrow \: 16 + 4a - 8 \\ \\ \tt \twoheadrightarrow \: 4a + 8 \dots(2) \\ \bf \: now \\ \\ \tt \twoheadrightarrow \: 2a - 4 = 4a + 8 \\ \\ \tt \twoheadrightarrow \: 2a - 4a = 8 + 4 \\ \\ \tt \twoheadrightarrow \: - 2a = 12 \\ \\ \tt \twoheadrightarrow \: a = \frac{ - 12}{2} \\ \\ \boxed{\tt \twoheadrightarrow \: a = - 6}$