Maggie L.

asked • 06/25/15

5x^2 - 7x+1 = 0

Compute the value of the discriminant and give the number of real solutions of the quadratic equation
 

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Mark M. answered • 06/25/15

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The discriminant of Ax2 + Bx + C = 0 is B2 - 4AC.
 
For 5x2 - 7x + 1 = 0, B2 - 4AC = (-7)2 - 4(5)(1) = 49 - 20 = 29
 
Since the discriminant is positive and not a perfect square, the equation has two real solutions that are irrational.
 
 
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Andrew M.

Note that the discriminant...  b2-4ac ... in a quadratic is the part that goes inside the square root in the quadratic formula where if ax2+bx+c=0 then x = (-b±√(b2-4ac)/2a
 
If the discriminant is negative we have two imaginary roots that are complex conjugates
If the discriminant is equal to zero .. b2-4ac=0 .. we have one real root where x=-b/2a
If the discriminant is greater than zero then we have two real roots
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06/25/15

Mark M.

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And if the discriminant is positive and a perfect square, then there are two real roots that are also rational.  
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06/26/15

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