Problem 4 Using the Discriminant

How many real-number solutions does 2 x 2 − 3 x = − 5  have ? 2 x squared , minus 3 x equals negative 5 , have , question mark

✓ Got It?

4. 1. How many real-number solutions does 6 x 2 − 5 x = 7 6 x squared , minus 5 x equals 7  have?
   2. Reasoning If a is positive and c is negative, how many real-number solutions will the equation a x 2 + b x + c = 0 eh x squared , plus b x plus c equals 0  have? Explain.

✓ Lesson Check

Do you know HOW?

Use the quadratic formula to solve each equation. If necessary, round answers to the nearest hundredth.

1. − 3 x 2 − 11 x + 4 = 0 negative 3 x squared . minus 11 x plus 4 equals 0
2. 7 x 2 − 2 x = 8 7 x squared , minus 2 x equals 8
3. How many real-number solutions does the equation − 2 x 2 + 8 x − 5 = 0 negative 2 x squared . plus 8 x minus 5 equals 0  have?

Do you UNDERSTAND?

4. Vocabulary Explain how the discriminant of the equation a x 2 + b x + c = 0 eh x squared , plus b x plus c equals 0  is related to the number of x-intercepts of the graph of y = a x 2 + b x + c . y equals , eh x squared , plus b x plus c .
5. Reasoning What method would you use to solve the equation x 2 + 9 x + c = 0 x squared , plus 9 . x plus c equals 0  if c = 14 ?  If  c = 7 ? c equals 14 question mark , cap if , c equals 7 question mark  Explain.
6. Writing Explain how completing the square is used to derive the quadratic formula.