# How do you find the value of the discriminant and state the type of solutions given #4a^2=8a-4#?

##### 1 Answer

Sep 15, 2017

#### Explanation:

#"rearrange the quadratic equating to zero"#

#rArr4a^2-8a+4=0larrcolor(blue)" in standard form"#

#"with "a=4,b=-8,c=4#

#Delta=b^2-4ac=(-8)^2-(4xx4xx4)#

#color(white)(xxxxxxxxx)=64-64=0#

#color(blue)"Types of solutions"#

#• " if "Delta>0" roots are real and different"#

#• " if "Delta=0" roots are real and equal"#

#• " if "Delta<0" roots are not real"#

#"here "Delta=0rArr" roots are real and equal"#

#color(blue)"As a check"#

#"solving "4a^2-8a+4=0#

#rArr4(a^2-2a+1)=0#

#rArr4(a-1)(a-1)=0#

#rArra=1" or "a=1larrcolor(red)" real and equal"#