Question

find the answer of question​

Answer 1

given equation,5√5x^2+30x+8√5=0

here a=5√5

b=30

c=8√5

to solve a equation by factorization method first we need to find the AC.

AC=5√5×8√5=

200.

find the factors of 200 whose product is 200 and whose sum =b

here b=30

20×10=200.

20+10=30.

now split the middle term.

=》5√5x^2+30x+8√5=0

=》5√5x^2+20x+10x+8√5=0

=》5x(√5x+4) + 2(√5x+4)=0

=》(5x+2)(√5x+4)=0

=》5x+2=0 (or) √5x+4=0

=》5x=-2 (or) √5x=-4

=》x=-2/5 (or) x=-4/√5.

therefore -2/5 and -4/√5 are the roots of the 5√5x^2+30x+8√5=0 equation.

Answer 2

Solution:

$\mathfrak{Equation \: given} : \\ \\ 5 \sqrt{5}x {}^{2} + 30x + 8 \sqrt{5} = 0$

By splitting the middle term:

Now,

Constant term× x^2 coefficient

=8√5 × 5√5

=200

Factors of 200:

200×1

100×2

50×4

25×8

20×10

Analysing the factors,we get 20+10=30

Thus, splitting the middle term with accordance to the suitable factors of 200.

Now,

5√5x^2+30x+8√5=0

=>5√5x^2+20x+10x+8√5=0

=>5x(√5x+4)+2√5(√5x+4)=0

=>(5x+2√5)(√5x+4)=0

=>5x+2√5=0 or √5x+4=0

=>x= -2√5/5 or x= -4/√5

The zeros are -2√5/5 and -4/√5.