If sum of square of zeros of quadratic equation f(x) = x2 – 8x + k

1.	If sum of square of zeros of quadratic equation f(x) = x2 – 8x + k is 40 then find the value of k.
Answer» Given polynomial f(x) = x² – 8x + k Let α and β are zeros of polynomial f(x) then Sum of zero (α + β) = - b/a = -(-8)/1 = 8 ....(i) and product of zeros (α x β) = c/a = k/1 = k ....(ii) Now, from equation (i) (α + β) = 8 Squaring both sides, (α + β)² = 8² ⇒ a² + β² + 2αβ = 64 …(iii) It is given that sum of square of zeros is 40. i.e., α² + β² = 40 Putting values from equation (i) and (ii) in (iii) 40 + 2k = 64 ⇒ 2k = 64 – 40 ⇒ 2k = 24 ⇒ k = 12 Thus k = 12

If sum of square of zeros of quadratic equation f(x) = x2 – 8x + k is 40 then find the value of k.

Answer»

Given polynomial f(x) = x² – 8x + k

Let α and β are zeros of polynomial f(x) then

Sum of zero (α + β) = - b/a

= -(-8)/1 = 8 ....(i)

and product of zeros

(α x β) = c/a = k/1 = k ....(ii)

Now, from equation (i)

(α + β) = 8

Squaring both sides,

(α + β)² = 8²

⇒ a² + β² + 2αβ = 64 …(iii)

It is given that sum of square of zeros is 40.

i.e., α² + β² = 40

Putting values from equation (i) and (ii) in (iii)

40 + 2k = 64

⇒ 2k = 64 – 40

⇒ 2k = 24

⇒ k = 12

Thus k = 12