Exercise 18 Page 77

Recall that sqrt(- a)= isqrt(a).

Roots: x= 12i and x=- 12i
Number and Type of Roots: two imaginary roots

Practice makes perfect

To solve the given equation, let's first isolate x^2.

4x^2+1=0

LHS-1=RHS-1

4x^2=-1

.LHS /4.=.RHS /4.

x^2=-1/4

Put minus sign in front of fraction

x^2=-1/4

We cannot find any real square roots of a negative number, so we will need to use the fact that sqrt(- a)= isqrt(a) to solve for x.

x^2=-1/4

sqrt(LHS)=sqrt(RHS)

x=± sqrt(- 1/4)

sqrt(- a)= isqrt(a)

x=± isqrt(1/4)

sqrt(a/b)=sqrt(a)/sqrt(b)

x=± isqrt(1)/sqrt(4)

Calculate root

x=± i 1/2

Commutative Property of Multiplication

x=± 1/2i

We found that the roots of the given equation are x= 12i and x=- 12i. Both of them are imaginary.

Exercises p.77-79

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