Determine the type of number that the solutions of x^2 +5x+3=0 will be
I have the answer as rational
is that right?
if your quadratic has rational roots then it would factor, it does not
Also the discriminant would have to be a perfect square for rational roots. It is not.
b^2 - 4ac = 25-4(1)(3) = 13
so you would have two different irrational roots
b^2-4ac= 25-12=13
and exactly what is sqrt 13? I took it to 13 digits, and didn't see numbers repeating. Why did you say rational?
2. A pool company will install a round swimming pool in the middle of a yard that measures 40 ft. by 20 ft. If the pool is 12 ft. in diameter, how much of the yard will still be available?: *
2x^3 -17x^2+47-42
no posible
To determine the type of number that the solutions of a quadratic equation will be, we can examine the discriminant (Δ). The discriminant is the expression inside the square root of the quadratic formula, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0).
In the case of the equation x^2 + 5x + 3 = 0, a = 1, b = 5, and c = 3. Therefore, we can calculate the discriminant as follows:
Δ = b^2 - 4ac
= (5)^2 - 4(1)(3)
= 25 - 12
= 13
If the discriminant is greater than 0, the solutions will be real and irrational. If the discriminant is equal to 0, the solutions will be real and rational. If the discriminant is less than 0, the solutions will be complex conjugates.
Since the discriminant in this case is Δ = 13, which is greater than 0, the solutions will be real and irrational, not rational. Therefore, your answer "rational" is not correct.