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Answer 1 · 2017-10-03T16:40:12

#20x^2-3x-9=0#

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#

Answer 2 · 2017-10-03T16:42:50

#20x^2-3x-9=0#

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