Question

Find the product and sum of the roots of the equation: 2x^2-9x-10=0

Answer 1

Answer:

          sum of the roots:    $x_1+x_2=4\frac12$

          product of the roots:     $x_1x_2=-5$            

Step-by-step explanation:

$2x^2-9x-10=0\quad\implies\quad a=2\,,\ b=-9\,,\ c=-10$

$b^2-4ac=(-9)^2-4(2)(-10)=81+80=161>0$

From Vieta's formulas applied to quadratic polynomial we have:

if    $b^2-4ac\geqslant0$   then

sum of roots:    $x_1+x_2=-\dfrac ba=-\dfrac{-9}2=4\frac12$

product of the roots:     $x_1x_2=\dfrac ca=\dfrac{-10}2=-5$