What is the maximum value of b for which the roots of 3x^2 + bx - 14 = 0 are real?
The roots of a quadratic equation of the form ax^2 + bx + c = 0 are real if `b^2 - 4ac >= 0`
For the equation 3x^2 + bx - 14 = 0, the roots are real when `b^2 - (4*3*-14) >= 0`
=> `b^2 >= -4*3*14`
This is true for all values of b as the square of a real number is always non-negative.
The equation 3x^2 + bx - 14 = 0 has real roots for all values of b