I think I worded the question a little bit weird lol, what I mean is, for example
m^2-8m+12=0 the answer to this equation is m=6 or m=2, correct? which obviously aren't the same number so they must have 2 different roots, but they are supposed to be EQUAL ROOTS? What am I missing?
m^2-8m+12=0 the answer to this equation is m=6 or m=2, correct? which obviously aren't the same number so they must have 2 different roots, but they are supposed to be EQUAL ROOTS? What am I missing?
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ONLY equations that are Perfect Square Trinomial have equa roots.
What are Perfect Square Trinomials. They are the answers to Binomials Squared.
Example
...............(3X-5)^2=.....(3X-5)(3X…
IF you had the equation.....9X^2-30X+25=0......to solve, the next step would be to factor first
(3X-5)(3X-5)=0..................set each factor to zero and solve
3X-5=0...........3X-5=0
3X=5...............3X=5
X=5/3..............X=5/3..............… ROOTS
NOW THERE IS A WAY TO TELL IF A QUADRATIC EQUATION WILL HAVE EQUAL ROOTS
Ax^2+Bx+C=0.......is the General Quadratic Equation where A is the coefficient of the x^2 term,
................................B is the coefficient of the x term, and C is the constant term (number)
IF.......B^2-4AC-0..........then the roots are equal (the same)
Try our example...
9X^2-30X+25
A=9..............B=-30.............C=2…
B^2-4AC=.......(-30)^2-4(9)(25)=......…
This equation has equal roots.................Knew it did also cause we solved it
I hope this helps
Have a GREAT MATH DAY.
What are Perfect Square Trinomials. They are the answers to Binomials Squared.
Example
...............(3X-5)^2=.....(3X-5)(3X…
IF you had the equation.....9X^2-30X+25=0......to solve, the next step would be to factor first
(3X-5)(3X-5)=0..................set each factor to zero and solve
3X-5=0...........3X-5=0
3X=5...............3X=5
X=5/3..............X=5/3..............… ROOTS
NOW THERE IS A WAY TO TELL IF A QUADRATIC EQUATION WILL HAVE EQUAL ROOTS
Ax^2+Bx+C=0.......is the General Quadratic Equation where A is the coefficient of the x^2 term,
................................B is the coefficient of the x term, and C is the constant term (number)
IF.......B^2-4AC-0..........then the roots are equal (the same)
Try our example...
9X^2-30X+25
A=9..............B=-30.............C=2…
B^2-4AC=.......(-30)^2-4(9)(25)=......…
This equation has equal roots.................Knew it did also cause we solved it
I hope this helps
Have a GREAT MATH DAY.
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Your additional details are confusing. What are you trying to solve? In the additional details you write x^2+(m+4)x+(4m+1)=0, where m is constant has equal roots which is a different equation that m^2 -8m + 12, which may or may not have equal roots--not all quadratic equations have equal roots.
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So the equation doesn't have equal roots!
m^2 - 8m + 16 = 0 WOULD have equal roots (m = 4)
but m^2 - 8m + 12 =0 ==> (m -6)(m-2) two distinnct roots.
m^2 - 8m + 16 = 0 WOULD have equal roots (m = 4)
but m^2 - 8m + 12 =0 ==> (m -6)(m-2) two distinnct roots.
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Square of coefficient of m minus 4*coefficient of m^2 *constant if equal to 0 then the roots are equal if more than 0 then the roots are distinct
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Some quadratics have equal roots but not all.
Here's one that does.
x²+6x+9=0
(x+3)(x+3)=0
x+3=0 or x+3=0
x=-3 or x=-3
As you rightly say, your example does not have equal roots.
Here's one that does.
x²+6x+9=0
(x+3)(x+3)=0
x+3=0 or x+3=0
x=-3 or x=-3
As you rightly say, your example does not have equal roots.
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Book can also make mistake.