Question

which of the following have real roots. a)2x²+x-1=0. b)x²+x+1=0. c)x²-6x+6=0. d)2x²+15x+30=0

Answer 1

The roots of the basic equation ax²+bx+c=0 are found with the quadratic formula.

$\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }$

While all letters are real, it is required that $\sqrt{b^2-4ac}$ is real.

There are three cases:

• Case 1. The square root of a negative number is imaginary.

• Case 2. The square root of 0 is zero.

• Case 3. The square root of a positive number is real.

a) Case 3, therefore real.

b) Case 1, therefore imaginary.

c) Case 1, therefore imaginary.

d) Case 1, therefore imaginary.

So choice a) is the correct answer.

Answer 2

Answer:

x^2 +x+1=10

Step-by-step explanation:

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