Question

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

Answer 1

`"roots are real and equal"`

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"`