Can anyone please help me to solve these add math questions?

1) It's given that 3 and m+4 are the roots of the quadratic equation x^2 +(n-1)x +6=0,
Where m and n are constants. Find the value of m and n .

2) A quadratic equation x^2 +4(3x+k)=0 , where k is a constant has roots p and 2p , p is not equal to 0.
- Find the value of p and k.
-hence form the quadratic equation which has roots p-1 and p+6.


Pls help me and show out your steps . Thanks

1

Jawapan

  • Pengguna Brainly
2016-02-26T20:56:45+08:00
1) x^2 +(n-1)x +6=0
    sor = - n + 1 , por = 6
    3 + m + 4 = - n + 1  , (3)(m+4) = 6 
    m = - n - 6               ,  3m + 12 = 6
    -2 = - n - 6               ,          3m = - 6
    n = - 4                     ,             m = - 2

2) 
x^2 +4(3x+k)=0
    x^2 + 12x + 4k = 0
    a = 1 , b = 12 , c = 4k
    sor = - 12 , por = 4k
    3p = - 12  , (p)(3p) = 4k
    p = - 4      , (-4)(-12) = 4k
                       4k = 48
                       k = 12
 
    p - 1 + (p + 6) = 2p + 5
                            = 2(-4) + 5
                            = - 8 + 5
                            = - 3
 
    (p-1)(p+6) = p^2 + 6p - p - 6
                      = p^2 + 5p - 6
                      = (-4)^2 + 5(-4) - 6
                      = 16 - 20 - 6
                      = - 10
 
    x^2 - sor x + por = 0
    x^2 + 3x - 10 = 0



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