How much of a difference can 1 make

Algebra Level 3

Suppose it is given that the quadratic equation x 2 + p x + q + 1 = x^2+px+q+1= has two roots who differ by 2 2 . Then the graph of y = x 2 + p x + q y=x^2+px+q crosses the x x axis how many times?

1 1 0 0 1 1 or 0 0 times, depending on their values 2 2

Tom Zhou by Tom Zhou , 21, Canada

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1 solution

Saurabh Gupta
Sep 21, 2014

A quadratic equation always has two roots. Thus the function crosses the x-axis twice. Would cross once only if the discriminant is 0 and wont cross x axis if the discriminant is negative.

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