Find the value of p for which the quadratic equations x(x-4)+p=0 has r

1.	Find the value of p for which the quadratic equations x(x-4)+p=0 has real roots
Answer» <P>x(x - 4) + p = 0 can be REWRITTEN as x^2 - 4x + p = 0, or (x^2 - 4x + 4) - 4 + p = 0. x^2 - 4x + 4 = (x - 2)^2 Thus, (x - 2)^2 = 4 - p. This equation yields real SOLUTIONS if and only if 4 - p >= 0 (since the square of a real number is NONNEGATIVE), so p <= 4.

Find the value of p for which the quadratic equations x(x-4)+p=0 has real roots

Answer»

<P>x(x - 4) + p = 0 can be REWRITTEN as x^2 - 4x + p = 0, or (x^2 - 4x + 4) - 4 + p = 0.

x^2 - 4x + 4 = (x - 2)^2

Thus, (x - 2)^2 = 4 - p. This equation yields real SOLUTIONS if and only if 4 - p >= 0 (since the square of a real number is NONNEGATIVE), so p <= 4.

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Find the value of p for which the quadratic equations x(x-4)+p=0 has real roots

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