If sum of squares of the zeroes of polynomial x2−4x+k is 8, find k. Select one: a. 3 b. −4 c. 1 d. 4 please explain it clearly
Answers
x^2 - 4x + k = 0
ax^2 - 4x + k = 0
a = 1 , b = -4 , c = k
put value of k
let k = 3
x^2 - 4x + k = 0
x^2 - x - 3x + k = 0
x (x - 1) -3 (x - 1) =0
x - 1 = 0 , x - 3 = 0
x = 1 , x = 3
add them
sum of zeroes = 1 + 3 = 4
that is not equal to 8
let k = -4
x^2 - 4x - 4 = 0
x^2 - 2x - 2x - 4 = 0
x (x - 2) -2 (x - 2) = 0
x - 2 = 0 , x - 2 = 0
x = 2 , x = 2
add them
sum of zeroes = 2 + 2 = 4
that is not equal to 8
let k = 1
d = b^2 - 4ac
d = -4 × -4 - 4 × 1 × 1
d = 16 - 4
d = 12 >
x = - b+- 12^1/2÷ 2×1
x = -(-4)+-2×3^1/2÷ 2
x = 4 + 2× 3^1/2÷2 or x = 4 - 2× 3^1/2÷2
x = 2 (2 + 3^1/2)÷2 or x = 2 (2 - 3^1/2)÷2
x = 2 + 3^1/2 or x = 2 - 3^1/2
add them
sum of zeroes = 2 + 3^1/2 + 2 - 3^1/2
= 2 + 2
= 4
let k = 4
x ^2 - 4x + 4 = 0
x^2 - 2x - 2x + 4 = 0
x (x - 2) - 2(x - 2) = 0
(x - 2) (x - 2) = 0
x - 2 = 0 , x - 2 = 0
x = 2 , x = 2
add them
sum of zeroes = 2+2=4
that is not equal to 8
hence it is not possible that the sum of the zeroes of the following polynomial is 8.