Question

Find the coefficient of x square and x in the product of (x-3)(x+7)(x-4)

Answer 1

Step-by-step explanation:

find the coefficient of x2 and x in the product of (x-3) (x+7) (x-4)

Method 1 :  

(x-3) (x+7) (x-4)

= (x+7) (x-3)(x-4)

= ( x + 7) (x² - 7x + 12)

= x³ - 7x² + 12x  + 7x² - 49x + 84

= x³ - 37x + 84

Coefficient of x² = 0   & x = -37

Method 2 :

(x-3) (x+7) (x-4)

roots are  3  , 4  &  - 7

Sum of roots  = Coefficients of x²/Coefficient of x³

=> 3 + 4 - 7 = Coefficients of x²/1

=> Coefficients of x² = 0

3*4  + 4*(-7)  + 3(-7)  = Coefficients of x/Coefficient of x³

=> 12 - 28 - 21 = Coefficients of x/1

=> Coefficients of x = -37

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Answer 2

Step-by-step explanation:

(x–3)(x+7)(x–4)

= x³–37x+84

coeff of x = –37

coeff of x²=0