what is the discriminant and how many solutions would this quadratic have?\n$x^{2}-6x + 9 = 0$\n0, no…

what is the discriminant and how many solutions would this quadratic have?\n$x^{2}-6x + 9 = 0$\n0, no solutions\n0, 1 solution\n72, 2 solutions\n-72, no solution

what is the discriminant and how many solutions would this quadratic have?\n$x^{2}-6x + 9 = 0$\n0, no solutions\n0, 1 solution\n72, 2 solutions\n-72, no solution

Answer

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, in $x^{2}-6x + 9=0$, $a = 1$, $b=-6$, $c = 9$.

Step2: Calculate discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a = 1$, $b=-6$, $c = 9$ into it: $\Delta=(-6)^{2}-4\times1\times9=36 - 36=0$.

Step3: Determine number of solutions

If $\Delta>0$, there are 2 solutions; if $\Delta = 0$, there is 1 solution; if $\Delta<0$, there are no real - solutions. Since $\Delta = 0$, there is 1 solution.

Answer:

0, 1 Solution