Question

Describe the nature of the roots for this equation

2x^2+5x-7=0


a.two real, rational roots
b.two real,irrational roots
c.two complex roots
d.one real,double root

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,\\√(D)=√(81)=9,\\ \\x_1=(-5-9)/(2\cdot 2)=-(14)/(4)=-3.5,\\ \\x_2=(-5+9)/(2\cdot 2)=(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.