Question

If the sum of square of zeros of a quadratic polynomial x square - 8 x + K is 40 then find the value of k

Answer 1

Answer:

$k = 12$

Step-by-step explanation:

Let α, β be the zeroes of the polynomial x² - 8x + k. Then

$\alpha + \beta = 8$

$\alpha \beta = k$

It is given that

${ \alpha }^{2} + { \beta }^{2} = 40$

$or \: {( \alpha + \beta )}^{2} - 2 \alpha \beta = 40$

$or \: {8}^{2} - 2k = 40$

$or \: 64 - 40 = 2k$

$or \: 2k = 24$

$or \: k = 12$