Find Value of A if there is one real solution

Question

For what value of a will this equation have only one real root:

$$(2a−5)x^2−2(a−1)x+3=0$$

Note: $x$ is a variable

If found that $a=4$ works, but there seems to be another solution. Any help?

Answer 1

A quadratic equation has equal roots or repeated roots , when it fulfills the condition that

$D=0$

Here $D$ is the discriminant of the quadratic given by $D=b^2-4a\cdot c$

Here , $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ and $c$ is the constant term .

Can you take it on from here ?

Answer 2

You can have only one solution if the discriminant is $0$, or if the coefficient of the $x^2$ term is $0$. $a=5/2$