Question

Find the zeroes of the quadratic polynomial Xsquare +7x+10 and verify the relationship b/w the zeros of the coefficients

Answer 1

Hey dear !!

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==> In the example

we have given that ,

p(x) = x² + 7x + 10

And we have to find the zeroes of this polynomial with relationship between the zeroes and the coefficient. So lets do it !!

First we will find the zeroes of the polynomial !

=> x² + 7x + 10

=> x² +5x + 2x + 10

=> x(x + 5) + 2( x + 5 )

=> (x + 5) ( x + 2) are the factors of the given polynomial .

If x + 5 = 0

∴ x = -5 is the zero of the given polynomial .

If x + 2 = 0

∴ x = -2 is the another zero of the polynomial .

Therefore, -5 and -2 are the zeroes of the given polynomial .

Now, relation between the zeroes and the coefficient.

Let, α = -5 and β = -2

We know that,

α + β = -b/a

-5 +(-2) = -7 = -b/a

Also,

α * β = c/a

-5* (-2) = 10 = c/a

Hence, the relation between the zeroes and coefficient verified .

Thanks !!

[ Be Brainly ]

Answer 2

Hey!

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x^2 + 7x + 10

Where,

a = 1
b = 7
c = 10

Splitting the middle term -:

x^2 + 5x + 2x + 10

(x^2 + 5x) + (2x + 10)

= x ( x + 5) + 2 ( x + 5)

= ( x + 2) (x +5)

Zeroes are =>

x + 2 = 0
x = -2

x + 5 = 0
x = -5

Now, we know,

Sum of zeroes = - b/a

-2 + (-5) = - 7

- 7 = -7

Product of zeroes = c/a

- 2 × - 5 = 10

10 = 10

Now, as the relation between zeroes and coefficients is verified!

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Hope it helps...!!!