SAT Math · Advanced Math
Nonlinear equations in one variable practice questions
Each free question on this page comes with its answer and a full explanation, and each one is marked easy, medium or hard.
- Question 10 · mediumFor what positive value of k does the equation x² - kx + 9 = 0 have exactly one real solution?
- Question 11 · hardThe equation x² - 7x + c = 0 has two real solutions that differ by 3. What is the value of c?
- Question 12 · mediumWhat value of x satisfies 8^x+1 = 32^x-2?
- Question 26 · mediumIf |2x - 5| = 11 and x is negative, what is the value of x?
- Question 33 · mediumWhat is the solution to √(2x+3) = x, after rejecting any extraneous candidate?
- Question 34 · mediumWhat is the sum of all values of x that satisfy 2^x²-5x = 2^-6?
- Question 63 · hardWhat is the sum of all real solutions to x^4 - 13x² + 36 = 0?
- Question 77 · mediumWhat is the solution to x+2/x-3 = 5/x-3?
- Question 78 · mediumHow many real solutions does the equation |3x - 6| = 2x have?
- Question 79 · hardThe polynomial x³ - 7x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?
- Question 95 · mediumThe equation 2^x = x + 5 can be solved by finding the x-coordinates where the graphs of y=2^x and y=x+5 intersect. How many real…
- Question 100 · mediumFor what negative value of k does the equation x² + kx + 16 = 0 have exactly one real solution?
- Question 117 · mediumThe equation 3^x = x + 10 has a positive real solution. Between which two consecutive integers does this positive solution lie?
- Question 131 · mediumFor how many integer values of k between -6 and 6, inclusive, does the equation x² + kx + 9 = 0 have exactly one real solution?
- Question 132 · hardFor what values of k does the equation x² + kx + 9 = 0 have two distinct real solutions?
- Question 136 · hardThe equation x² - bx + 24 = 0 has two real solutions whose difference is 5. What is the value of b, given that both solutions…
- Question 151 · mediumWhat value of x satisfies 4^x-1 = 8^x+2?
- Question 156 · mediumHow many valid solutions does the equation √(x+10) = x - 2 have, after rejecting any extraneous candidates?
- Question 157 · hardThe polynomial x³ - 4x² - 7x + 10 has x=1 as one of its roots. What is the product of the other two roots?
- Question 175 · mediumWhat is the larger of the two solutions to |4x - 8| = 3x?
- Question 185 · mediumIf |3x + 1| = 13 and x is positive, what is the value of x?
- Question 192 · mediumWhat is the sum of all real solutions to 3^x² - 2x = 3^8?
- Question 195 · mediumWhat is the solution to (3x+1)/(x-4) = 2, given that x ≠ 4?
- Question 196 · hardThe equation x² - 9x + c = 0 has two real solutions that differ by 5. What is the value of c?
- Question 212 · hardFor what values of k does the equation x² + kx + 16 = 0 have two distinct real solutions?
- Question 216 · mediumWhat value of x satisfies 9^x+2 = 27^x-1?
- Question 218 · hardThe polynomial x³ - 2x² - 5x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?
- Question 233 · hardThe equation x² - 11x + c = 0 has two real solutions that differ by 7. What is the value of c?
- Question 235 · hardThe polynomial x³ + 2x² - 5x - 6 has x = 2 as one of its roots. What is the sum of the other two roots?
- Question 255 · mediumWhat value of x satisfies 5^x+3 = 25^x-2?
- Question 256 · hardThe equation x² - 13x + c = 0 has two real solutions that differ by 3. What is the value of c?
- Question 273 · mediumWhat is the sum of all real solutions to |5x - 10| = 3x?
- Question 276 · hardThe polynomial x³ - 3x² - 6x + 8 has x = 1 as one of its roots. What is the sum of the other two roots?
- Question 292 · hardThe equation x² - 10x + c = 0 has two real solutions that differ by 4. What is the value of c?
- Question 293 · hardThe polynomial x³ + x² - 10x + 8 has x = 1 as one of its roots. What is the sum of the other two roots?
- Question 310 · hardThe polynomial x³ - 4x² - x + 4 has x = 1 as one of its roots. What is the sum of the other two roots?
- Question 314 · hardThe equation x² - 15x + c = 0 has two real solutions that differ by 7. What is the value of c?