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Question
Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x2 + x + 2
Solution
y = x2 + x + 2
y = x2 + x + 2 ......(1)
Compare this equation with the equation
ax2 + bx + c = 0
We have a = 1 , b = 1, c = 2
b2 – 4ac = 12 – 4 × 1 × 2 = 1 – 8
b2 – 4ac = – 7 < 0
Since the discriminant is negative the quadratic equation has no real roots and therefore the graph does not meet x-axis.
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