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Nature of Solutions Graphically

Graph of y=x2...

Question

Graph of $y = x^{2} + 7 x + 3$ intersects the x-axis at __ number of points

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Solution

$y = x^{2} + 7 x + 3$

a = 1, b = 7, c = 3

$D = b^{2} - 4 a c = 49 - 4 (1) (3)$

= 49 - 12 = 37 > 0

As D > 0, the roots will be real & distinct

So, graph of given expression touches the x-axis at 2 points.

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