Question

Find the zeros of the quadratic polynomial x×x +7x+10, and verify the relationship between the zeros and the coefficient.

Answer 1

$hey \: mate \: here \: is \: your \: answer...$

$x {}^{2} + 7x + 10$
${x}^{2} + (5 + 2)x + 10$
${x}^{2} + 5x + 2x + 10$
$x(x + 5) + 2(x + 5)$
$(x + 2)(x + 5)$
$two \: zeros \: of \: the \: polynomial \\ are \: - 2 \: and \: - 5$



$verification...$

$sum \: of \: zeros = \frac{ - b}{a}$
$- 2 + ( - 5) = \frac{ - 7}{1}$

$- 2 - 5 = - 7$
$- 7 = - 7$



$product \: of \: zeros = \frac{c}{a}$

$- 2 \times - 5 = \frac{10}{1}$

$10 = 10$

$hence \: verified...$





$hope \: it \: helps.....$

Answer 2

x²+5x+2x+10=0. =>ax²+bx+c=0. a=1 ,b=7 ,c=10
x(x+5)+2(x+5)=0
(x+2)(x+5)=0
x=-2 or x=-5
alpha x beta = c/a. alpha+beta = -b/a
-2 x -5=10/1. -2+(-5)=-(7)/1
10= 10. -7=-7