Question

8. Find the sum of the zeroes of quadratic polynomial x² + 7x + 10.​

Answer 1

Step-by-step explanation:

x² + 7x + 10.

we know sum of zeroes =-b/a

so,-7/1

=》-7..

therefore -7 is the sum of the zeroes of quadratic polynomial x² + 7x + 10.

Factoring  x2+7x+10 

The first term is,  x2  its coefficient is  1 .

The middle term is,  +7x  its coefficient is  7 .

The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 10 = 10 

Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   7 .

     -10   +   -1   =   -11     -5   +   -2   =   -7     -2   +   -5   =   -7     -1   +   -10   =   -11     1   +   10   =   11     2   +   5   =   7   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  5 

                     x2 + 2x + 5x + 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                    x • (x+2)

              Add up the last 2 terms, pulling out common factors :

                    5 • (x+2)

Step-5 : Add up the four terms of step 4 :

                    (x+5)  •  (x+2)

             Which is the desired factorization

x =-5 & -2.

therefore by adding -5 & -2. we will get -7 which is the sum of zeroes of x² + 7x + 10.

Answer 2

As the question,

${x}^{2} + 7x + 10 = 0 \\ = > {x}^{2} + 2x + 5x + 10 = 0 \\ = > x(x + 2) + 5(x + 2) = 0 \\ = > (x + 5)(x + 2) = 0 \\ = > x = - 5 \: \: or \: \: x = - 2$

Hence, the sum of the zeroes = -7

Another method:

$\frac{ - 7}{1} = \frac{ - constant \: of \: x}{constant \: of \: {x}^{2} } = - 7$

HOPE THIS COULD HELP!!!