Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Determine the number of real roots of the quadratic equation 6x2−5x+105=06x^2 - 5x + 105 = 06x2−5x+105=0.
How many real roots does the equation x2+x+1=0x^2 + x + 1 = 0x2+x+1=0 have?
Find the number of real roots of the quadratic x2−4x+4=0x^2 - 4x + 4 = 0x2−4x+4=0.
How many real roots does the quadratic x2+2x+5=0x^2 + 2x + 5 = 0x2+2x+5=0 have?
Find the number of real roots of the quadratic 7x2+14x+7=07x^2 + 14x + 7 = 07x2+14x+7=0.
Determine how many real roots the equation 10x2+3x−1=010x^2 + 3x - 1 = 010x2+3x−1=0 has.
Determine the number of real solutions of 12x2−x+3=012x^2 - x + 3 = 012x2−x+3=0.
Determine the number of real roots of 5x2−20x+20=05x^2 - 20x + 20 = 05x2−20x+20=0.
Determine the number of real solutions of 2x2−8x+6=02x^2 - 8x + 6 = 02x2−8x+6=0.
How many real solutions does 4x2−4x+1=04x^2 - 4x + 1 = 04x2−4x+1=0 have?
Find how many real roots the quadratic 3x2+6x+2=03x^2 + 6x + 2 = 03x2+6x+2=0 has.
Find the value of kkk such that the quadratic equation kx2+2x+1=0kx^2 + 2x + 1 = 0kx2+2x+1=0 has exactly one real root.
Determine the range of kkk for which the equation kx2+2x+1=0kx^2 + 2x + 1 = 0kx2+2x+1=0 has two distinct real roots.
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Question Type 2: Finding solutions to quadratic inequalities by converting into ax^2+bx+c > or < 0 and checking intervals
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Question Type 4: For a quadratic dependent on a parameter, finding the value of the parameter that results in either situation of roots