Question

Find the zeroes of the polynomial x2 +10x+21 and verify the relationship between the zeroes and the coefficients

Answer 1

Answer:

hi mate hope my answer finds u in the pink of your health--

Step-by-step explanation:

given p (x)=x^2+10x+21

x^2+10x+21=0

x^2+7x+3x+21=0

x(x+7)+3 (x+7)=0

(x+7)(x+3)=0

implies, x=-7 or x=-3.

therefore the zeroes of p (x) are -7 and -3

now the sum of zeroes = -7-3 = -10.

on comparing the given polynomial with the standard form we get, a=1,b=10,c=21.

now -b/a= -10/1 =-10 which is equal to sum of roots.

now product of roots = (-7)×(-3)=21

c/a =21/1=21 =product of roots.

so the relationship between the zeroes and co-efficients are founded.

hope this helps you

be happy

keep smiling: )

Answer 2

Answer:

The zeroes are -3 and -7 and the relationship between the zeroes and coefficient are founded.

Step-by-step explanation:

P (x) = x² + 10 x + 21

To find the zeroes, we will put P(x) = 0. We get that:

x² + 10 x + 21 = 0

By using middle term splitting, we get that:

x² + 7 x + 3 x + 21 = 0

x ( x + 7 ) + 3   ( x + 7 ) = 0

( x + 7 ) ( x + 3 ) = 0

Solving it, we get that:

x = - 7     or     x = - 3 .

The zeroes of p (x) are -7 and -3

Now, the relation between the zeroes need to be established:

Sum of zeroes = - 7 - 3 = -10.

We will be comparing the given polynomial with the standard form:

a = 1

b = 10

c = 21.

- b / a = -10 / 1 = -10

which is also equal to the sum of roots.

Also, the product of roots = (-7 ) × (- 3) = 21

c / a = 21 / 1 = 21

which is also the product of roots.

Therefore, the zeroes are -3 and -7 and the relationship between the zeroes and coefficient are founded.

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