Question

find the zeros of the function $f(x) = 1.7x^2 - 6.5x + 2$. round values to the nearest thousandth (if necessary).

Explanation:

Step1: Identify quadratic formula

For \( ax^2 + bx + c = 0 \), roots are \( x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 1.7 \), \( b=-6.5 \), \( c = 2 \).

Step2: Calculate discriminant

\( D=b^2 - 4ac=(-6.5)^2-4\times1.7\times2=42.25 - 13.6 = 28.65 \)

Step3: Find roots

\( x_1=\frac{-(-6.5)+\sqrt{28.65}}{2\times1.7}=\frac{6.5 + 5.3526}{3.4}=\frac{11.8526}{3.4}\approx3.486 \)
\( x_2=\frac{-(-6.5)-\sqrt{28.65}}{2\times1.7}=\frac{6.5 - 5.3526}{3.4}=\frac{1.1474}{3.4}\approx0.337 \)

Answer:

The zeros are approximately \( x \approx 0.337 \) and \( x \approx 3.486 \)