1-AND PRODUCTION sum of roots of the equation :X²-X-6=0

Question

2-FOR what values of A the equation has no solution ax ² +3 x-7 = 0
3-For what values of x the equation has 2 solution X²-X+C=0
4-Solve the equation (X-1)²-4=0
5-Solve the equation a)2/2 x^(-3)=2√2
b)3^(x^2-2x)=27
c)5/25 x^(+3)=5√5
help me with the solution of this equations please

Answer 1

1.
Factor the equation to
(x-3)(x+2)=0
So the roots are 3 and -2.
Calculate the sum of roots.
2.
A quadratic equation ax²+bx+c=0 has no real roots when the discriminant is less than zero, that is:
b²-4ac<0
For the present case,
b=3, c=-7
Solve for the inequality in terms of a.

3. and up
Please show some work to indicate where you have difficulties.

Answer 2

a)2/2 x^(-3)=2√2
b)3^(x^2-2x)=27
c)5/25 x^(+3)=5√5
i have difficulties with this three equations

Answer 3

a)
2/(2x^(-3))=2√2
2/(2x^(-3)) = 2√2/1
Cross multiply to get:
2*1 = (2√2)*(2x^(-3))
1=2√2/x³
Cross multiply again:
x³=2√2
x³=(√2)³
Can you take it from here?

b)
3^(x^2-2x)=27
3^(x^2-2x)=3³
therefore
(x^2-2x)= 3
Solve for x by factoring
x²-2x-3=0
(x-3)(x+1)=0
...
c)
similar to a).
Post your answer for checking if you wish.