Question

find the zeros of the function $f(x) = 2x^2 - 6.7x - 2$. round values to the nearest thousandth (if necessary). answer attempt 1 out of 2

Explanation:

Step1: Recall Quadratic Formula

For a quadratic function \( f(x) = ax^2 + bx + c \), the zeros are given by \( x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 2 \), \( b=-6.7 \), \( c = -2 \).

Step2: Calculate Discriminant (\( D \))

Discriminant \( D=b^2 - 4ac \). Substitute values:
\( D=(-6.7)^2-4\times2\times(-2) \)
\( D = 44.89+16 \)
\( D = 60.89 \)

Step3: Apply Quadratic Formula

First, for the plus sign:
\( x_1=\frac{-(-6.7)+\sqrt{60.89}}{2\times2}=\frac{6.7 + 7.803}{4}=\frac{14.503}{4}=3.62575\approx3.626 \)
Second, for the minus sign:
\( x_2=\frac{-(-6.7)-\sqrt{60.89}}{2\times2}=\frac{6.7 - 7.803}{4}=\frac{-1.103}{4}=-0.27575\approx - 0.276 \)

Answer:

The zeros of the function are \( x\approx3.626 \) and \( x\approx - 0.276 \)