Question

for the given equation, state the value of the discriminant and the number of real solutions. 25x² - 20x + 4 = 0 the discriminant is 0. (simplify your answer. type an integer or a decimal.) there is/are 1 real solution(s). (type a whole number.)

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c=0$, here $a = 25$, $b=-20$, $c = 4$.

Step2: Calculate discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute values: $\Delta=(-20)^{2}-4\times25\times4=400 - 400=0$.

Step3: Determine number of real - solutions

If $\Delta>0$, 2 real solutions; if $\Delta = 0$, 1 real solution; if $\Delta<0$, 0 real solutions. Since $\Delta = 0$, there is 1 real solution.

Answer:

The discriminant is 0. There is 1 real solution.