Question

find the zeros of the polynomial x^2+7x-8 and verify the relationship between the zeros and the coefficient

Answer 1

Hello friends☺️☺️

Here is your answer :

${x}^{2} + 7x - 8$

To find Zeroes

${x}^{2} + 7x - 8 = 0$

${x}^{2} + 8x - x - 8 = 0$


$x(x + 8) - 1(x + 8) = 0$



$(x + 8)(x - 1) = 0$



$x + 8 = 0 \: \: \: \: \: or \: \: \: \: x - 1 = 0$


$x = - 8 \: \: \: \: or \: \: \: \: x = 1$


Zeroes are - 8 and 1.


Sum of Zeroes :

$\alpha + \beta = - 8 + 1$


$= - 7$


$= \frac{ - (7)}{1}$


$= \frac{ - b}{a}$




Product of Zeroes :

$\alpha \beta = ( - 8)(1)$

$= - 8$


$= \frac{ - 8}{1}$


$= \frac{c}{a}$



Hence, verified.


Hope it helps you...

Answer 2

Hey dear !!!

____________________________


==> In the example ,

we have,

p(x) = x² + 7x - 8

And we have to find zeroes of the given polynomial. So , lets do it !!!!

=> Given :

=> x² + 7x - 8

=> x² + 8x - x - 8

=> x(x + 8 ) - 1( x + 8 )

=> ( x + 8 ) ( x - 1) are the factors of the given polynomial .

If x + 8 = 0

∴ x = -8 is the zero of the polynomial

If x - 1 = 0

∴ x = 1 is the zero of the polynomial

Therefore, -8 and 1 are the zeroes of the given polynomial .

Now, relation between the zeroes and the coefficient.

Let, α = -8 and β = 1

We know that,

α + β = -b/a

-8 + 1 = -7/1 = -b/a

Also,

αβ = c/a

-8* 1 = -8/1 = c/a

Therefore, relation between the zeroes and the coefficient is verified .

Thanks !!!

[ Be Brainly ]