Question

find the quadratic polynomial ,x to the power 2 -2x-8 and vrify the realtionship between zeros and their co-efficents of the polynomial

Answer 1

See the attach file for ans

Answer 2

$\underline\mathfrak{Given:-}$

• x² - 2x - 8

$\underline\mathfrak{To \: \: Find:-}$

• Find the zeroes are coefficients ......?

$\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: P \: {(x)} \: \: = \: \: {x}^{2} \: - \: {2x} \: - \: {8}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: - \: {2x} \: - \: {8}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: - \: {4x} \: + \: {2x} \: - \: {8}$

$\: \: \: \: \: \leadsto \: \: {x} \: {({x} \: - \: {4})} \: + \: {2} \: {({x} \: - \: {4})}$

$\: \: \: \: \: \leadsto \: \: {({x} \: + \: {2})} \: \: \: {({x} \: - \: {4})}$

$\: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {-2} \: \: \: and \: \: \: {x} \: \: = \: \: {4}$

$\: \: \: \: \: \: \: \: \: {\alpha} \: \: = \: \: {-2} \: \: \: and \: \: \: {\beta} \: \: = \: \: {4}$

$\underline\mathfrak{Verification:-}$

x² - 2x - 8

• a = 1
• b = -2
• c = -8

$\: \: \: \: \: \therefore {Sum \: \: of \: \: zeroes} \: \: = \: \: \frac{ \: - \: coefficient \: \: of \: \: x}{coefficient \: \: of \: \: {x}^{2}}$

$\: \: \: \: \: \leadsto \: \: {\alpha} \: + \: {\beta} \: \: = \: \: \frac{-b}{a}$

$\: \: \: \: \: \leadsto \: \: {-2} \: + \: {4} \: \: = \: \: - \: \frac{(-2)}{1}$

$\: \: \: \: \: \leadsto \: \: {2} \: \: = \: \: {2}$

$\: \: \: \: \: \therefore {Product \: \: of \: \: zeroes} \: \: = \: \: \frac{constant \: \: term}{coefficient \: \: of \: \: {x}^{2}}$

$\: \: \: \: \: \leadsto \: \: {\alpha} \: {\beta} \: \: = \: \: \frac{c}{a}$

$\: \: \: \: \: \leadsto \: \: {-2} \: \times \: {4} \: \: = \: \: {\frac{-8}{1}}$

$\: \: \: \: \: \leadsto \: \: {-8} \: \: = \: \: {-8}$

Verified.