Question

if sum of square of zeroes of quadratic polynomial f(x) =x²-2x-k is 20 then find the value of k
​

Answer 1

Answer:-

Given Polynomial : x² - 2x - k.

Let , a = 1 , b = - 2 and c = - k.

Let the zeroes of the equation be α and β.

We know that,

Sum of the zeroes = - b/a

→ α + β = - ( - 2) / 1

→ α + β = 2 -- equation (1)

Product of the zeroes = c/a

→ αβ = k / - 1

→ αβ = - k -- equation (2)

Also given that,

Sum of squares of the zeroes = 20

→ α² + β² = 20 -- equation (3)

We know that,

(a + b)² = a² + b² + 2ab

Hence,

( α + β )² = α² + β² + 2αβ

Putting the values from equations (1) , (2) & (3) we get,

→ (2)² = (20) + 2 * ( - k)

→ 4 = 20 - 2k

→ 4 - 20 = - 2k

→ - 16 = - 2k

→ - 16/ - 2 = k

→ k = 8

Therefore, the value of k is 8.