Question

Which of the following equations only have one solution? x2+4x+4=0, x2+x=0, x2-1=0

Answer 1

x2+4x+4=0

Explanation:

To find the number of real roots for a quadratic, we apply the discriminant. The discriminant is the inside portion of the square root from the quadratic formula.

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`b^2-4ac>0` yields 2 real roots

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`b^2-4ac=0` yields 1 real root

• [tx]b^2-4ac<0[/tex] yields no real roots

x2+4x+4=0 has a = 1, b = 4 and c = 4. So 4^2 - 4(1)(4) is 16 - 16 = 0. This yields 1 root.

x2+x=0 has a = 1 and b = 1 and c = 0. So 1^2 - 4(1)(0) = 1- 0 = 1. This yields 2 roots.

x2-1=0 has a = 1 and b = 0 and c= -1. So 0^2 -4(1)(-1) = 0 + 4 = 4. This yields 2 roots.