Question

Describe the nature of the roots for this equation

Answer 1

First, fint the roots of the equation $2x^2+5x-7=0.$

1.

$D=5^2-4\cdot 2\cdot (-7)=25+56=81,\\\sqrt{D}=\sqrt{81}=9,\\ \\x_1=\dfrac{-5-9}{2\cdot 2}=-\dfrac{14}{4}=-3.5,\\ \\x_2=\dfrac{-5+9}{2\cdot 2}=\dfrac{4}{4}=1.$

2. You can see that this equation has two different real roots. Note that you can make this statement without finding roots, only knowing the value of discriminant: since D=81>0, then the equation has two different real roots.