Answer:
[tex]b^2-4ac>0[/tex] yields 2 real roots
Step-by-step explanation:
To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.
• [tex]b^2-4ac>0[/tex] yields 2 real roots
• [tex]b^2-4ac=0[/tex] yields 1 real root
• [tx]b^2-4ac<0[/tex] yields no real roots
Example:
[tex]4x^2-7x+2=0[/tex] where a=4, b=-7, and c=2
[tex]b^2-4ac=(-7)^2-4(4)(2)=49-32=17<0)[/tex].
It has 2 real roots
