Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients. X^2-8-2x

Answer 1

Answer:

the zeroes are 4, -2

sum of zeroes =-b/a

product of zeros= c/a

Answer 2

Answer:

➡➡your ans☢☢☢

Step-by-step explanation:

$\bf\ let \: p(x) = {x}^{2} - 2x - 8 \\ \\ \bf\ zero \: of \: the \: polynomial \: is \: the \: value \: of \: x \: where \: p(x) = 0 \\ \\ \bf\ putting \: \: p(x) = 0 \\ \\ \bf\ \implies{x}^{2} - 2x - 8 = 0 \\ \\ \bf\red{ \underline{using \: the \: splitting \: term \: method}} \\ \\ \bf\green{\underline{where \: sum \: of \: the \: two \: numbers = - 2}} \\ \\ \bf\pink{ \underline{and \: product \: of \: the \: two \: numbers = - {8x}^{2} }} \\ \\ \bf\orange{so \: the \: numbers = 4x \: and \: 2x} \\ \\ \bf\ \implies {x}^{2} - (4x - 2x) - 8 = 0 \\ \\ \bf\ \implies {x}^{2} - 4x + 2x - 8 = 0 \\ \\ \bf\ \implies \: x(x - 4) + 2(x - 4) = 0 \\ \\ \bf\ \implies \: (x - 4)(x + 2) = 0 \\ \\ \bf\red{ \underline{ \mapsto: x - 4 = 0}} \\ \\ \bf\red{ \underline{ \implies \: x = 4}} \\ \\ \bf\blue{ \underline{ : \mapsto \: x + 2 = 0}} \\ \\ \bf\blue{ \underline{x = - 2}} \\ \\ \bf\ therefore \: \alpha = - 2 \: and \: \beta = 4 \: are \: the \: zeros \: of \: the \: polynomial \\ \\ \bf\ \: p(x) = {x}^{2} - 2x - 8 \\ \\ \bf\ \implies1 {x}^{2} - 2x - 8 \\ \\ \bf\ comparing \: with \: {ax}^{2} + bx + c \\ \\ \bf\ \: so \: a = 1 \: \: b = - 2 \: \: c = - 8 \\ \\ \bf\red{ \: sum \: of \: zeros \implies - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }} \\ \\ \bf\ i.e = \alpha + \beta = \frac{ - b}{a} \\ \bf\{ \underline{ \mapsto: l.h.s = \alpha + \beta = - 2 + 4 = 2 }\\ \bf\{ \underline{ \mapsto: r.h.s = - \frac{b}{a} = - \frac{ - 2}{1} = 2 }\\ \\ \bf\purple{product \: of \: zeros \implies \frac{constant \: term}{coefficient \: of \: {x}^{2}} } \\ \\ \bf\ \mapsto:i.e = \alpha \times \beta = \frac{c}{a} \\ \bf\ \mapsto:l.h.s = \alpha \beta =( - 2) ( 4) = - 8 \\ \bf\ \mapsto: \frac{c}{a} = \frac{ - 8}{1} = - 8 \\ \\ \\ \bf\red{ \underline{ \mapsto:since \: l.h.s =r .h.s} }\\ \\ \bf\orange{ \underline{ \mapsto:hence \: relationship \: between \: zeros \: and \: coefficient \: is \: proved}}$

$\large\boxed{ \fcolorbox{pink}{lime}{hope \: it \: help \: you}}$