Quadratics with no real solutions

​Complex Numbers-No Real Solutions

​Graphs:

​A graph of an equation has no real solution if there is no point of intersection on the graph between the curve itself and the x-axis.

​The equation y=x^2+1 does not intersect the x -axis. Therefore, no value of x will satisfy the equation x^2+1=0 . Thus, this equation has no real solution.

​Using Algebra:

Does the equation y=x^2+1 have a real solution? (Start by setting y=0)

Multiple Choice

Does y=2x^2−8 have a real solution(s)? If so, what are they?

• Yes, {-2, 2}

• Yes, {2}

• No real solutions

• Yes, {0, -3}

Multiple Choice

Does
−x^2−2x=1 have a real solution(s)?

• No real solutions

• Yes, {1, 0}

• Yes, -1

• Yes, {-1, 1}

Multiple Choice

Does 5x^2+3=2x^2−5 have a real solution(s)?

• Yes, {-8, 3}

• Yes, {-8}

• No real solution

• Yes, -8/3

​Systems:

Is there an x value that can make both equations true at the same time?

​How many real solutions?

You can solve graphically or algebraically.

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How many real roots (solutions) does this graph have have?

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How many real roots (solutions) does this graph have?

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How many real solutions does 2x^2−4=−3x^2 have?