Which quadratic equation has no real roots?

Choose exactly two answers that are correct.

–x2 + 2x – 6 = 0

–2x2 + 3x + 4 = 0

2x2 + x – 6 = 0

2x2 – x + 3 = 0

A and D

Step-by-step explanation:

By finding the roots of all the equations, we see that options A and D are the only ones that require an imaginary number in order to solve

The first choice and the last have no real roots.

Step-by-step explanation:

For an equation to have no real roots the value of the discriminant ( b^2 - 4ac) will be negative.

Working out the values:

1.  D = (-2)^2 - 4* -1*-6 = -20 so it has no real roots.

2. D = (3)^2 - 4*  -2* 4 =  41 so it does have real roots.

3. D = (1)^2 - 4* 2*-6 = 49 so real roots.

4. D =   (-1)^2 - 4* 2*3 = -23 so  no real roots

b

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: