Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...

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y = ax^{2} + bx + c
To find zeros of the quadratic function use formula: x_{12} = (- b ± √D) / (2a) , D = b^{2} - 4ac
In the set of real numbers: 1. There are two zeros, if D > 0 2. There is one zero, if D = 0 3. There is no zeros, if D < 0
Let's find value of x if y = 0
4x^{2} + 6x - 2 = 0 ---> 2x^{2} + 3x - 1 = 0
D = 3^{2} - 4*2*(-1) = 17 > 0 x_{1} = (-3 + √17) / 4 x_{2} = (-3 - √17) / 4

Heather G. | Math and Geosciences TutorMath and Geosciences Tutor

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Adding to what Mark said, you can graph the equation too (either by hand or with the aid of a graphing calculator) to check that what you have solved using the Quadratic equation is correct. You'll be able to see if and where the function crosses the x-axis.

Mark D. | Become an Expert: Specializing in Math, Physics, Stats and SAT prepBecome an Expert: Specializing in Math, ...

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Just a hint but the x-intercept is where the graph crosses the x-axis so ask yourself what value does "y" have when this occurs. You can directly use the Quadratic equation and solve for values of x for this special case. If the values are real numbers then they exist.