Answer:
No zeros
Explanation:
we have to solve the equation x² – 8x + 17 = 0 ,in order to determine The zeroes of f.
Method 1 :
x² – 8x + 17 = 0
The discriminant Δ = (-8)² – 4 × 1 × 17 = 64 − 68 = −4
Since Δ < 0 then the equation has no solutions
Thus, f has no zeros.
Method 2 :
x² – 8x + 17 = x² – 2(x)(4) + 16 – 16 + 17
= x² – 2(x)(4) + 16 – 16 + 17
= x² – 2(x)(4) + 4² – (17 - 16)
= (x - 4)² + 1
Then
x² – 8x + 17 = 0
⇔ (x - 4)² + 1 = 0
⇔ (x - 4)² = -1 (impossible)
Which means ,f has no zeros.