Question

If a,b,c are 3 factors of p cube -7p+6 then Value of a+b+c

Answer 1

Answer:

we know that

sum of zeros of a cubic polinomial :

α+β+∝ = -b/a

so,

a+b+c = -(-7)/1

a+b+c = +7

Step-by-step explanation:

Answer 2

The value of a+b+c is 0

Therefore a+b+c=0

Step-by-step explanation:

Given equation is $p^3-7p+6$

Also given that a,b and c are factors of the given expression

To find the value of a+b+c :

First find the values of a ,b and c

Given equation can be written as

$p^3+0p^2-7p+6$

Since a,b and c are factors of $p^3+0p^2-7p+6$ then we can write

$p^3+0p^2-7p+6=0=(p-a)(p-b)(p-c)$

• To solve the cubic equation by synthetic method :

$p^3+0p^2-7p+6=0$

1  _|  1      0       -7      6

        0      1         1     -6

     ________________

        1       1        -6     0

Therefore p-1 is a factor

Now we have the quadratic equation $p^2+p-6=0$

• Now solving the quadratic equation

$p^2+p-6=(p+3)(p-2)=0$

$(p+3)(p-2)=0$

p+3=0 or p-2=0

p=-3 or p=2

Therefore p+3 and p-2 are also the factors

Therefore the given expression can be written as

$p^3-7p+6=(p-1)(p+3)(p-2)$

• Comparing the above equation with $p^3+0p^2-7p+6=0=(p-a)(p-b)(p-c)$ we get

(p-a)(p-b)(p-c)=(p-1)(p+3)(p-2)

(p-a)(p-b)(p-c)=(p-1)(p-(-3))(p-2)

Therefore the values are a=1 , b=-3 and c=2

• Now find the value of a+b+c

Substitute the values we get

a+b+c=1-3+2

=3-3

=0

Therefore a+b+c=0

The value of a+b+c is 0