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Without trying to solve the equation 3x^2-5x+7=0, how would you know that it has no real roots?

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please help
asked May 4, 2014 in ALGEBRA 1 by anonymous

2 Answers

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Best answer

The solutions of a quadratic equation ax2 + bx + c = 0, a ≠ 0, can be classified as follows.If the discriminant b2 - 4ac is


1. positive, then the quadratic equation has two distinct real solutions and its graph has two - intercepts.


2. zero, then the quadratic equation has one repeated real solution and its graph has one - intercept.


3. negative, then the quadratic equation has no real solutions and its graph has no - intercepts.

The quadratic equation is 3x2 - 5x + 7 = 0.

Compare the equation 3x2 - 5x + 7 = 0 with general form of quadratic equation ax2 + bx + c = 0, a ≠ 0.

a = 3, b = - 5 and c = 7.

The discriminant =  b2 - 4ac = (- 5)2 - 4(3)(7) = 25 - 84 = - 59 < 0.

Here discriminant is negative, so the quadratic equation has no real roots.

answered May 6, 2014 by steve Scholar
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The equation image

Compare it to quadratic form image

image

Roots are image

image

image

image

The roots of image are imaginary.

image

No real roots for image.

answered May 5, 2014 by david Expert

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