C1-Algebra basics and Quadratic equations
Expand 3(x+2).
3x + 6
Solve: x^4+3x^2-4=0
Real root of x=+/-1
Derive the quadratic formula from ax^2+bx+c=0.
x=(-b+/-root(b^2-4ac)/2a
Solve 15=5x
x=3
Solve 3/x=5/(x+2).
x=3
Solve 7x-20=2x-5
x=3
Solve: 3x^2 -18x +1=0
x=3 +/-root(26/3)
Solve (8x-1)/(x+2)=5.
x=3 2/3
Solve: 2x^2-x-3=0
x=3/2 or -1
Solve 7/(5x-3)=2/(x+1).
x=4 1/3
Solve 18=6x-7
x=4 1/6
Expand -2(3a-2)(4a-1).
=-2(12a^2-3a-8a+2)=-2(12a^2-11a-3)=-24a^2+22a-4
Expand -5a(4a^2 - 2a + 1).
=-20a^3+10a^2-5a
Solve (3x/5)-2x=4.
x=-2 6/7
Solve 3=(15x+2)/4x.
x=-2/3
Solve 4-7x=x-12
x=2
Solve 5x+4=14
x=2
Solve 8/x=4.
x=2
Solve x+10=12
x=2
Solve 7=(3-4x)/(2x-5)
x=2 1/9
Solve 7-5(3x-4)=3-(2x+5)
x=29/13=2 3/13
Solve: 4+3x=x^2
x=4 or -1
Solve: x^2-8x=2
x=4+/-3root2
Solve 2x=10
x=5
Solve: 2x^2-10x-3=0
x=5/2 +/-root(31)/2
Solve: 3x^2/3 -5x^1/3 +2=0
x=8/27 or 1
Expand (5x-2)(x-2)(2x-1).
=(5x-2)(2x^2-x-4x+2)=(5x-2)(2x^2-5x+2)=10x^3-25x^2+10x-4x^2+10x-4=10x^3-29x^2+20x-4
Label the parts of:x^2-x=3x-6.
Terms: x^2, -x, 3x and -6 Expressions (2 or more terms put together): x^2-x and 3x-6 Equations: x^2-x=3x-6
An equation is...
Where an expression is not the same as another term or expression once factorised, expanded or simplified; therefore a value of x can be found e.g. x+3=7 This is expressed using the = sign.
Find the value of k for which x^2+kx+9=0 has different roots.
k<-6 or k>6
Find the value of k for which kx^2-4x+1=0 has equal roots.
k=4
Find the value of k for which x^2+6x+k=0 has no real roots.
k>9
Solve 3x^2-8x+2=0
x=(4+/-root10)/3
Solve: x^2-9=0
x=-3 or 3
Solve (3x-2)/4-(x-2)/3=(2x-1)/6.
x=-4
Solve 3(2x-1)=4(x-2).
x=-5/2=-2 1/2
Solve: 10x^2 + 5x=0
x=0 or -1/2
Solve: x^2=3x
x=0 or 3
Solve 5-3/2x=4.
x=1 1/2
Solve (4x-7)/10=(x-3)/5.
x=1/2
Solve 5-3x=4.
x=1/3
Solve 5x-3/4=x+2
x=11/16
Solve (5x-3)/4=2.
x=11/5=2 1/5
Expand (4-5x)^2.
=16-40x+25x^2
Expand (x^2+3x-2)(2x^2-1).
=2x^4-x^2+6x^3-3x-4x^2+2=2x^4+6x^3-5x^2-3x+2
Expand 5 -2(5x-3).
=5 - 10x + 6=11-10x
Expand 2(3x^2-6x-1)-(x^2-4x+2).
=6x^2-12x-2-x^2+4x-2=5x^2-8x-4
Expand (3+2x)^2.
=9+12x+4x^2
Expand (3x-5)^2.
=9x^2-30x+25
Expand (x+3)^2.
=x^2+6x+9
Expand (x+4)^2.
=x^2+8x+16
Expand (x-6)^2.
=x^2-12x+36
Expand (x+2)(x-3).
=x^2-3x+2x-6=x^2-x-6
Expand (x-3/2)^2.
=x^2-3x+9/4
A quadratic equation...
Has different roots (if discriminant is >0) Has one root (if discriminant is 0) Has no (real) roots (if discriminant is <0)
The discriminant of a quadratic equation ax^2+bx+c...
Is b^2-4ac
An identity...
Is where one expression is exactly the same as another, once expanded, simplified or factorised; so a value of x cannot be found. e.g. 3x+3 = 3(x+1)This can be expressed using a triple equals sign.
Solve 6=17-7x.
x=11/7=1 4/7
Solve x/3=4.
x=12
Solve 8=x-5
x=13
Solve x-5=8
x=13
