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laneycasey9058
30.12.2020 •
Mathematics
A) by completing the square find in the form of the constant p the roots of the equation x^2+px+4=0 b) hence find the set of values of p for which the equation has no real roots
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Ответ:
a)
b) p is in the interval (-4,4)
Step-by-step explanation:
Quadratic Equation
It's given the following quadratic equation:
a)
It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:
We already have the first term squared, and we need to find the second term. Rewriting the equation:
The second term of the binomial is 1/2p, thus completing the squares with
:
Factoring:
Moving the independent term to the right side:
Taking the square root:
Solving for x:
b) If the equation won't have real roots, then the radicand should be negative:
Factoring:
The zeros of the left-side polynomial are:
p = 4
p = -4
The inequality:
Is satisfied for values of p in the interval (-4,4)
Ответ: