Question: Solve by graphing the related function of the equation - x2 - 2x + 3 = 0.
A ) 3 and 1
B ) - 3 and 1
C ) - 7 and 6
D ) - 3 and 3
Steps to derive
1 - x2 - 2x + 3 = 0 is written in standard form as y = - x2 - 2x + 3.
2 Sketch the graph of the quadratic function y = - x2 - 2x + 3 as:
3 From the graph, the x-intercepts are - 3 and 1.
[Estimate the values of the x-intercepts.]
4 - (- 3)2 - 2(- 3) + 3 = 0
[Substitute x = - 3 in the equation - x2 - 2x + 3.]
5 0 = 0
[Simplify.]
6 - (1)2 - 2(1) + 3 = 0
[Substitute x = 1 in the equation - x2 - 2x + 3.]
7 0 = 0
[Simplify.]
8 Both the values satisfy the equation. So, - 3 and 1 are the roots of the equation.
Hence the right answer is Option B
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