Question

Tell how many solutions the equation has. $$ 3 x^{2}-7 x+5=0 $$

Short answer

The quadratic equation \(3x^{2}-7x+5=0\) has no real solutions

Step-by-step solution

Identify the coefficients a, b, and c

The quadratic equation is in the form \(ax^{2}+bx+c=0\). Here, \(a=3\), \(b=-7\), and \(c=5\).

Calculate the discriminant

Use the formula \(b^{2}-4ac\) to calculate the discriminant. So here, it is \((-7)^{2}-4*3*5 = 49-60 = -11\)

Determine the number of solutions

As the discriminant is less than 0 (-11), it implies that the quadratic equation has no real solutions.