Identify the number and type of solutions for the equation x^2 − 7x + 3 = 01 real 2 real 1 nonreal complex 2 nonreal complex

Accepted Solution

Answer:2 realStep-by-step explanation:To answer this question, we need to know whether the discriminant is positive, negative, or zero. The discriminant is the part of the quadratic equation that is under the square root.Quadratic Equation:  -b±√(b²-4ac)/(2) b²-4ac is the discriminantThe equation is already in Standard Form, so now we need to find the a, b, and c values.Standard Form: [tex]0 = ax^{2} +bx+c[/tex][tex]x^{2} -7x+3 = 0[/tex]A = 1 (since an imaginary 1 is in front of the variable)B = -7C = 3Now we substitute these numbers into the discriminant ( b²-4ac ):(-7)²-4(1)(3)-7²= 494(1)(3) = 12So, we have 49-12 = 37This is a positive result! (37)A positive discriminant = two real solutionsA discriminant of zero = one real solutionA negative discriminant = zero real solutions (it would equal nonreal complex solutions instead) I hope this helps!