Question

find the sum of the Zeroes and the product of the zeroes of the quadratic polynomial 2 x square - 10x + 12​

Answer 1

Step-by-step explanation:

2x²-10x+12

2x²-6x-4x+12

2x(x-3)-4(x-3)

(x-3)(2x-4)

One zero is x = 3

x - 3 = 0

x = 3

Second zero is x = 2

2x-4 = 0

2x = 4

x = 4/2

x = 2

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

TO DETERMINE

The sum of the Zeroes and the product of the zeroes of the quadratic polynomial

$2 {x}^{2} - 10x + 12$

CALCULATION

The given Quadratic polynomial is

$2 {x}^{2} - 10x + 12$

Comparing with

$a {x}^{2} + bx + c$

We get

$a = 2 \: , \: b = - 10 \: , \: c = 12$

So

$\sf{Sum \: of \: the \: Zeroes \: } = \displaystyle \: - \frac{b}{a} = - ( - \frac{10}{2} ) = 5$

$\sf{Product \: of \: the \: Zeroes \: } = \displaystyle \: \frac{c}{a} = \frac{12}{2} = 6$