Question

hey there..!


Find the zeros of the quadratic polynomial x^2 + 7x + 10 and verify relationship between the zeros and the coefficients.

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Answer 1

Hello brainlygirl
Here is your answer.

equation is x² + 7x + 10
so now we will find its roots of zeroes.

=> x² +7x + 10
=>x² + 5x +2x +10
=> x(x + 5) + 2(x + 5)
=> (x+2) (x+5)
hence the zeroes of question are
-2 and -5

now if you need to verify this zeroes is correct or not just put these on equation. you will find equation comming is zero.
Hence verified.

I hope it helps

Answer 2

solution


$Let f (X) = x^2 + 7x + 10$



Here we splitting the middle term then we find.

$f (X) = x^2 + ( 5+2)x + 10$


[ 7 = 5+2 and 5 ×2 = 10 ]


$f (X) = x^2 + 5x+2x + 10 \\ = X ( X +5)+2(X+5)$

f(X) = ( X +5)(X+2)

on putting f (X ) =0 , we get

( X +5)(X+2) = 0

X +5 = 0 or X + 2 =0

X = -5

or

X = -2

since the zeros of the given formula are.

$\alpha = - 5 \\ \\ and \\ \\ \beta = - 2$

Verification

Now


$Here \: sum \: of \: zeros , \\ \\ α+ β = - 7 = \frac{coefficients of X }{coefficients of x^2} \\ \\ and product of zeros \: \\ \\ \alpha \beta = 10 = \frac{Constant term}{Coefficients of x^2}$


Therefore the relationship Between the zeros and the coefficients is verified.



Be brainly