Question

find the zeros of the following quadratic polynomial and verify the relation between the zeros and the coefficient

2x^2+5x+2
​​

Answer 1

$= {2x}^{2} + 5x + 2$

$= {2x}^{2} + (4 + 1)x + 2$

$= 2 {x}^{2} + 4x + x + 2$

$= 2x(x + 2) + 1(x + 2)$

$= (2x + 1)(x + 2)$

$x + 2 = 0$

$x = - 2$

$2x + 1 = 0$

$2x = 1$

$x = \frac{1}{2}$

$sum \: \: of \: \: zeros \: : - 2 + \frac{1}{2}$

$= \frac{ - 3}{2}$

$product \: \: of \: zeros: - 2 \times \frac{1}{2}$

$= \frac{ - 2}{2}$

=1

Answer 2

Step-by-step explanation:

=2x

2

+5x+2

= {2x}^{2} + (4 + 1)x + 2=2x

2

+(4+1)x+2

= 2 {x}^{2} + 4x + x + 2=2x

2

+4x+x+2

= 2x(x + 2) + 1(x + 2)=2x(x+2)+1(x+2)

= (2x + 1)(x + 2)=(2x+1)(x+2)

x + 2 = 0x+2=0

x = - 2x=−2

2x + 1 = 02x+1=0

2x = 12x=1

x = \frac{1}{2}x=

2

1

sum \: \: of \: \: zeros \: : - 2 + \frac{1}{2}sumofzeros:−2+

2

1

= \frac{ - 3}{2}=

2

−3

product \: \: of \: zeros: - 2 \times \frac{1}{2}productofzeros:−2×

2

1

= \frac{ - 2}{2}=

2

−2

=1