Question

Find zeros of the polynomial x²-18x+12 and verify the rrlationship between zeros and coefficient of variable inthe polynomial​

Answer 1

Step-by-step explanation:

$given \: p(x) = {x}^{2} - 8x + 12$

$= {x}^{2} - 2x - 6x + 12$

$= x(x - 2) - 6(x - 2)$

$(x - 2)(x - 6)$

x -2 = 0

•°• x = 2

x - 6 = 0

•°• x = 6

$\alpha = 2 \\ \beta = 6$

$sum \: of \: zeroes = s \\ s = \alpha + \beta \\ s = 2 +6 \\ s = 8 \\ \frac{ - b}{a} = \frac { - ( - 8)}{1} \\ \frac{ - b}{a} = 8 \\ \\ s = \frac{ - b}{a} \\ hence \: verified$

$product \: of \: zeroes = p \\ p = \alpha \beta \\ p = 6 \times 2 \\ p = 12 \\ \frac{c}{a} = \frac{12}{1} \\ \frac{c}{a} = 12 \\ \\ p = \frac{c}{a} \\ hence \: verified$

Adiós! Hope this helps you.