EQUATIONS

Question 1

SUBSTITUTION PROPERTY

Answer 1

if a=b then a may replace b or b may replace a

e.g. x+3=y and x=z then

z+3=y

Question 2

linear equation

Answer 2

ax+b=0

Question 3

linear equations can be solved by

Answer 3

isolating the variable, the answer is the solution of the set

Question 4

quadratic equations

Answer 4

ax²+bx+c=0

e.g. x²+2x=0 and 5=x²

Question 5

quadratic equations can be solved by

Answer 5

a. factoring the given into binomials and equating them to 0
b. completing the square method
write ax²+bx+c=
as ax²+bx=-c

1. multiplying the whole equation by the value of 4a
2. add the value of b² afterwards
3. left hand side into a pst

c. quadratic formula
x=(-b±√b²−4ac)/2a

Question 6

the sum of the roots of a quadratic equation without solving for the roots is

Answer 6

r₁+r₂=−b/a

Question 7

product of the roots of a quadratic equation without solving for it is

Answer 7

r₁×r₂ =c/a

Question 8

quadratic equation

another equation for ax²+bx+c =0, a is not equal to 0 is

Answer 8

x²+(b/a x) + (c/a) = 0
or 
x² − (r₁+r₂)x + (r₁×r₂) =0
or 
(x-r₁) (x-r₂)=0

Question 9

The nature of roots is given by its discriminant

Answer 9

D=b²−4ac
whereas
*D>0, roots are real and unequal
- if D is a perfect square then the roots are rational
- if D is not a perfect square, then the roots are irrational conjugates
*if D=0, roots are real and equal
- roots are called double root
*if D < 0 , the roots are conjugate complex numbers