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What is the maximum value of b for which the roots of 3x^2 + bx - 14 = 0 are real?

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grade82 | Student | eNoter

Posted July 2, 2013 at 5:51 AM via web

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What is the maximum value of b for which the roots of 3x^2 + bx - 14 = 0 are real?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 2, 2013 at 5:55 AM (Answer #1)

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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

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