Given, quadratic polynomial is f(𝑥) = 𝑥² − 8𝑥 + 𝑘

Let a and b are the zeroes of the polynomial

Again given, the sum of the squares of zeroes of the quadratic polynomial = 40

=> a² + b² = 40

=> (a + b)² - 2ab = 40

=> 8² - 2ab = 40          {from the polynomial}

=> 64 - 2ab = 40

=> 2ab = 64 - 40

=> 2ab = 24

=> ab = 24/2

=> ab = 12

Now, product of the roots = k/1

=> 12 = k/1

=> k = 12

So, the value of k is 12