How many solutions does the quadratic y=3x2+2x+1 have? Reference Sheet - Number of Solutions of Quadratic Equation (1 point) Responses Two real number solutions Two real number solutions One real number solution One real number solution No real number solutions No real number solutions

Answer 1

To determine the number of solutions for the quadratic equation \( y = 3x^2 + 2x + 1 \), we can use the discriminant from the quadratic formula, which is given by:

\[ D = b^2 - 4ac \]

In the equation \( ax^2 + bx + c = 0 \), we identify:

• \( a = 3 \)
• \( b = 2 \)
• \( c = 1 \)

Now we can calculate the discriminant:

\[ D = (2)^2 - 4(3)(1) = 4 - 12 = -8 \]

Since the discriminant \( D \) is negative (\( D < 0 \)), this means that the quadratic equation has:

• No real number solutions.

Therefore, the correct response is No real number solutions.