9.+Quadratic+Equations

Exercise 41.


The "±" means you need to do a plus AND a minus, and therefore there are normally TWO solutions. The blue part (**b2 - 4ac**) is called the "discriminant", because it can "discriminate" between the possible types of answer. If it is positive, you will get two real solutions, if it is zero you get just ONE solution, and if it is negative you get complex solutions. Now that you know the equation you have to look for the three letters which are A=5,B=15,C=0, in the problem.  After that all you have to do is plug them in the equation. After that is going to sound like this.. x equal negative 15 plus AND a minus, under the radical line 15^2 minus 4 times 5 and 0, divide by 2 times 5. Solve it and it simplify like this x equals negative 15 plus AND minus root 225, divide by 10, which equals negative 15 plus AND minus the root 15 because is the root of 225, divided by 10.  Than you take 15 out of the root, and it sound like this .. negative 15 plus 15, divided by 10, which equals 0/10=0 or negative 15 minus 15, divided by 10, equals negative -30/10= -3. The answer is (N=0,-3). Enjoy =).

Exercise 42.


The first __#|step__ of this is to add 25 on both sides to get rid of zero so that the variable and coefficent and equal something. When you subtract, you are left with 4x^2=25. To get rid of the 4 in front of the x so that x can equal something, we divide by 4 on both sides. 4x^2/4 turns into just x^2 when you cancel out 4. 25/4 cannot be reduced further as a fraction. We are left with x raised to the power of 2. To undo this, we have to find the square root of both 25 and 4. The fraction turns into 5/2. X=+/-5/2

or x = (-5/2), (5/2)

[[image:e45.jpg width="577" height="68"]]
First you start with the Pythagorean formula (a² = b² + c²) a= hypotenuse b= side c= side so then it would be, 11^2=7^2+x^2 when you square root it, you will have 121=49+x^2 then you subtract 49 on each side and get 72 x^2=72, you square root the 72 and get (6square root2)

x=(6square root2)

Exercise 48.
first you must draw a right triangle, place the cm where it belongs. l 6 H l_90____ 4 1) you need to use the formula a^2+b^2=h^2

2) plug in the numbers 6^2+4^2=H

3) solve the equation 6^2=36 and 4^2=16

4) now you must add the centimeters 36 and 16 which gives you 52. the answer may be negative or positive, therefore your answer is +- radical 52.