Question #9b2b7

2 Answers
Oct 3, 2017

20x^2-3x-9=0

Explanation:

Let roots be a=-3/5 and b=3/4
Sum of Roots a+b=-3/5+3/4=3(1/4-1/5)=3/20
Multiplication of roots ab=-3/5xx3/4=-9/20

If the roots of Quadratic equation is a and b then the equation will be

x^2-("sum of roots")x+("Multiplication of roots")=0
x^2-(a+b)x+ab=0
x^2-3/20x-9/20=0

Multiply whole equation by 20
20x^2-3x-9=0

Oct 3, 2017

20x^2-3x-9=0

Explanation:

If we work backwards starting by letting x equal the two roots. Then make the equation equal to 0.

x=-3/5
x+3/5=0
5x+3=0

x=3/4
x-3/4=0
4x-3=0

Now these equations equal 0 we can put them into the factorised form of a quadratic.

(5x+3)(4x-3)=0

Expand.

20x^2-15x+12x-9=0
20x^2-3x-9=0

So 20x^2-3x-9=0 is the quadratic with roots -3/5 and 3/4