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math

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

  • math - ,

    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.

  • math - ,

    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

  • math - ,

    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.

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