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Solving equations

FinnManley

Find the value k for which 5x^2-2x+k=0 has exactly one solution.

What should i do to work this out

Reply 1

thekidwhogames

If it has one solution, that means the roots are equal hence b^2-4ac=0. Plug that in and solve.

Reply 2

Shaanv

Are u familiar with the roots of a quadratic.

For a quadratic ax^2+bx+c

If b^2-4ac>0 then the quadratic has two real roots.

If b^2-4ac=0 then the quadratic has 1 real root.

If b^2-4ac<0 then the quadratic has no real roots.

Reply 3

FinnManley

Original post by thekidwhogames

If it has one solution, that means the roots are equal hence b^2-4ac=0. Plug that in and solve.

Thanks that has worked.

Reply 4

FinnManley

Original post by Shaanv

Thanks, am i right in saying k=1/5

Reply 5

ghostwalker

Original post by FinnManley

Thanks, am i right in saying k=1/5

Yes.

Reply 6

Dalek1099

Original post by FinnManley

Thanks, am i right in saying k=1/5

Yes thats correct. An alternative solution is to note that if a quadratic has just one solution then that means it can be written in the form a(x+b)^2 e.g it has no constant term when completing the square and this will easily give you the value of k.