Quadratic Roots (1 Viewer)

[Menomaths]

Hey guys, searched all over youtube and not a single decent explanation for quadratic roots...
Here's the question(I know it's simple but I have no concept );
The roots of a quadratic equation ax^2 -bx- 10 = 0 are -1 and 5. Find the values of a and b.
Thanks.

 

[NFmusic1995]

easy, so you know -b / a is the sum of roots ie -1 + 5 = -1
And the product of roots is C/a , i.e -1 x 5 = -5

So we know alpha + beta = -4
and (alpha)(beta) = -5

So you simultaneous equations and find a and b i think

 

[Menomaths]

easy, so you know -b / a is the sum of roots ie -1 + 5 = -1
And the product of roots is C/a , i.e -1 x 5 = -5

So we know alpha + beta = -4
and (alpha)(beta) = -5

So you simultaneous equations and find a and b i think

Sub what into what? We already know alpha and beta
I got to find the sum and product of the roots, don't know what to do after

 

[Parvee]

An easier way is to just sub in the roots to get two equations and solve simultaneously to get a and b.
a=2, b=8

 

[Menomaths]

An easier way is to just sub in the roots to get two equations and solve simultaneously to get a and b.
a=2, b=8

What do I sub in and where do I sub in

 

[Parvee]

What do I sub in and where do I sub in

okay you know the roots are x=-1, x=5 and your equation is ax^2-bx-10=0
subbing in x=-1
a+b-10=0 ....(1)
subbing in x=5
25a-5b-10=0
5a-b-2=0 ....(2)

 

[Menomaths]

okay you know the roots are x=-1, x=5 and your equation is ax^2-bx-10=0
subbing in x=-1
a+b-10=0 ....(1)
subbing in x=5
25a-5b-10=0
5a-b-2=0 ....(2)

You can sub the roots into a and b =o never knew that. Thanks

 

[Parvee]

You can sub the roots into a and b =o never knew that. Thanks

Nope, the roots are the x values

 

[AnimeX]

I think there's ambiguity whether a is the letter "a" or alpha.

 

[SharkeyBoy]

Hey guys, searched all over youtube and not a single decent explanation for quadratic roots...
Here's the question(I know it's simple but I have no concept );
The roots of a quadratic equation ax^2 -bx- 10 = 0 are -1 and 5. Find the values of a and b.
Thanks.

ax^2-bx-10 = 0 roots = -1, 5
Sum of roots = 4
Product of roots = -5
Sum of roots = (-b/a),
since b is -b and a is a, sum of roots = b/a
Product of roots = (c/a)
since c is -10 and a is a, product of roots = -10/a
now we have two simultaneous equations:
b/a = 4
-10/a = -5
solving this, we get a = 2, b = 8

 

[Drongoski]

OR

For this question: -1 & 5 are the roots of the quadratic equation: a(x+1)(x-5) = 0

i.e. of a(x² - 4x -5) = 0

Comparing the 2 quadratics: a = 2 and b = 8

 

[Menomaths]

Thanks for letting me know all these methods guys!