Find the discriminant of the quadratic $3x^2 - 7x + 6.$
2 answers:
Answer:
Discriminant of the quadratic is-23
Step-by-step explanation:
The given quadratic function is 
Comparing with the expression 
a = 3, b = -7, c = 6
The discriminant of the quadratic is given by 
Substituting the known values, discriminant of the quadratic is

Therefore, discriminant of the quadratic is-23
Solve for x:
3 x^2 - 7 x + 6 = 0
Divide both sides by 3:
x^2 - (7 x)/3 + 2 = 0
Subtract 2 from both sides:
x^2 - (7 x)/3 = -2
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -23/36
Write the left hand side as a square:
(x - 7/6)^2 = -23/36
Take the square root of both sides:
x - 7/6 = (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
x = 7/6 + (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(23))/6 or x = 7/6 - (i sqrt(23))/6
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