Let and be the roots of the quadratic equation 2x^2 - 8x + 7. Find 1/(2a) +1/(2b)
+2498 \(\text{use the quadratic formula :} \\x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
here is the roots:
+9673 Don't use the quad. formula because i have a faster way.
In the quad. eq. ax2+bx+c=0
Sum of the 2 sol. = \(-\frac{b}{a}\)
Product of the 2 sol. = \(\frac{c}{a}\)
a and b are the 2 roots of the equation in your question.
Let's make it \(\alpha\)and\(\beta \)
\(\frac{1}{2\alpha}+\frac{1}{2\beta}\)
= \(\frac{\alpha+\beta}{2\alpha\beta}\)
=\(\frac{-\frac{-8}{2}}{\frac{(2)(7)}{2}}\)
= \(\frac{4}{7}\)
