# If A, B and C are three roots of x 3 – 7x + 6 = 0 then the value of A+

| If A, B and C are three roots of x

^{3}– 7x + 6 = 0 then the value of A+B+C is:A. x

B. 3

C. 3x

D. 0

### Right Answer is: D

#### SOLUTION

Let A, B and C are three factors of x^{3} – 7x + 6 = 0.

Now, compare this with standard three degree quadratic equation;

px^{3 }+ qx^{2 }+ rx + t = 0

sum of roots;

A + B + C = -q/p = 0/1 = 0

**Method: 2**

(x-a)(x-b)(x-c) = x^{3} – 7x + 6

now, putting x = 1 in the equation,

= 1^{3} – 7×1 + 6

= 0

So, (x-1) is a factor of the equation.

Now, dividing the given equation by (x – 1)

= (x^{3} – 7x + 6) ÷ (x – 1)

we get,

= x^{2} + x – 6

= x^{2} + 3x – 2x -6

= (x+ 3)(x-2)

So, we get three factors as, (x-1) (x+3) (x-2)= (x-a) (x-b) (x-c)

we get, a = 1, b = -3, c = 2

a + b + c = 1-3+2 = 0

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If A, B and C are three roots of x 3 – 7x + 6 = 0 then the value of A+