4) – 2x2 + 6x + 5 = 0 a. nonreal
b. real, irrational, and unequal
c. real, rational, and equal
d. real, rational, and unequal

b. real, irrational, and unequal

Step-by-step explanation:

Roots of a quadratic equation

The standard representation of a quadratic equation is:

where a,b, and c are constants.

Solving with the quadratic formula:

The argument of the radical is called the discriminant:

The nature of the solutions of the equation depends on the value of d as follows:

We are given the equation:

Here: a=-2, b=6, c=5. The discriminant is:

d = 116

Since d is positive and a non-perfect square, the roots are:

b. real, irrational, and unequal

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct