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

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)

step-by-step explanation:

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: