Bluebook SAT Test Nonlinear Equations and Systems 9

Question 1

What is the sum of the roots of the equation 3x² − 12x + 7 = 0?

Accepted Answer

4

Answer

By Vieta's formulas, sum of roots = −b/a = −(−12)/3 = 4.

Question 2

Which of the following equations has no real solutions?

Accepted Answer

x² + 3x + 10 = 0

Answer

For x² + 3x + 10 = 0, discriminant = 9 − 40 = −31 < 0, so no real solutions.

Question 3

If f(x) = x² − 6x + 8, at which x-value does the function reach its minimum?

Accepted Answer

x = 3

Answer

The vertex x-coordinate = −b/(2a) = 6/2 = 3.

Question 4

The parabola y = x² + 4x − 12 crosses the x-axis at two points. What is the product of those x-intercepts?

Accepted Answer

−12

Answer

By Vieta's formulas, product of roots = c/a = −12/1 = −12.

Question 5

Which of the following is a correct factored form of 6x² + 11x − 10?

Accepted Answer

(2x + 5)(3x − 2)

Answer

(2x + 5)(3x − 2) = 6x² − 4x + 15x − 10 = 6x² + 11x − 10. ✓

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