Question

If the sum of the zeroes of the polynomial f(x)= x2 -8x+k is 40, find value of k

Answer 1

Given :

• Equation = x² - 8x + k
• Sum of zeroes = 40

To Find :

• Value of k

Solution :

$\large\tt sum \: of \: zeroes = \frac{ - b}{a}$

Here

• a = 1
• b = - 8
• c = k

Substitute the value in formula

$\implies \tt \frac{ - ( - 8)}{k} =40 \\ \\ \implies \tt \frac{ 8}{k} =40 \\ \\ \implies \tt \frac{1}{k} = \frac{40}{8} \\ \\ \implies \tt \frac{1}{k} = 5 \\ \\ \large\boxed{ \tt k = \frac{1}{5} }$

Required equation :

$\tt {x}^{2} - 8x - \frac{1}{5} = 0 \\ \\ \tt \frac{5 {x}^{2} - 40x - 1}{5} = 0 \\ \\ \tt{x}^{2} - 40x - 1 = 0$