SAT Math Practice Questions-Passport to advanced mathematics-Solving quadratic equations

Question

Which of the following functions has a maximum value of \(m\), where \(m\) is a positive constant?

  1. f(\(x\))=\(m\)\(x\)2
  2. f(\(x\))=-\(m\)\(x\)2
  3. f(\(x\))=-\(x\)2+\(m\)
  4. f(\(x\))=-(\(x\)+\(m\))2
Answer/Explanation

Ans: C

Question

2\(x\)2-3\(x\)-7=0

If \(c\) and \(d\) are the two solutions of the quadratic equation above, what is the value of \(c\)+\(d\) ?

Answer/Explanation

Ans: 1.5, 3/2

Question

(\(x\)+2)= (\(x\)-5)(\(x\)+2)

What is the sum of the solutions to the given equation ?

Answer/Explanation

Ans: 4

Question

\(x\)2+10=91

What is the positive solution to the given equation?

  1. 9
  2. 10
  3. 41
  4. 51
Answer/Explanation

Ans: A

Question

\(x\)2-2\(x\)-1=0

The equation above has solutions \(x\)= \(n\)+\(\sqrt{k}\) and \(x\)= \(n\)-\(\sqrt{k}\), where \(n\) and \(k\) are positive integers. What is the value of \(n\)+\(k\)? 

Answer/Explanation

Ans: 3

Question

3\(x\)2+\(x\)-2=0

The solutions to the quadratic equation above are \(a\) and \(b\). what is the value of \(a\)+\(b\)?

  1. \(\frac{-5}{3}\)
  2. \(\frac{-1}{3}\)
  3. \(\frac{1}{3}\)
  4. \(\frac{5}{3}\)
Answer/Explanation

Ans: B

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