Question

5x^2-4-8x
Find zeros of polynomial and verify relationships between the zeros and coefficient

Answer 1

Given:-

p(x)=0

→5x²-8x-4=0

$\rule{200}{1}$

To find:-

→Find the Zeros of polynomial and verify the relationship b/w its coefficient?

$\rule{200}{1}$

Proof:-

→5x²-8x-4=0

๛S=-8[Sum of Equation]

๛P=-20[Product of Equation]

-10×2=-20

-10+2=-8

→5x²-10x+2x-4=0

→5x(x-2)+2(x-2)=0

๛5x+2=0

๛x-2=0

$\rule{200}{1}$

•Taking x-2

→x-2=0

๛x=2→(α)

$\rule{200}{1}$

•Taking 5x+2

→5x+2=0

→5x=-2

๛x=$\frac{-2}{5}$→(β)

$\rule{200}{1}$

a=5,b=-8,c=-4

→α+β=$\frac{-b}{a}$

→2+(-⅖)=$\frac{-(-8)}{5}$

[°•° Cross Multiply LHS]

→$\frac{10-2}{5}$=$\frac{8}{5}$

→$\frac{8}{5}$=$\frac{8}{5}$

✓erified

$\rule{200}{1}$

→αβ=$\frac{c}{a}$

→2×(-⅖)=$\frac{-4}{5}$

→-⅘=-⅘

✓erified

$\rule{200}{2}$

Answer 2

Answer:

$5x {}^{2} - 8x - 4 = 0 \\ 5x {}^{2} - 10x + 2x - 4 = 0 \\ 5x(x - 2) +2(x - 2) \\ (x - 2)(5x + 2) \\ x = 2 \\ x = - \frac{2}{5} \\ \\ therefore \\ \alpha = 2 \\ \beta = - \frac{2}{5} \\ \\ here \: \\ a = 5 \: \: \: \: b = - 8 \: \: \: \: c - 4 \\ \\ sum \: of \: zeroes = \alpha + \beta = - \frac{b}{a} \\ \alpha + \beta = - \frac{ - 8}{5} \\ 2 - \frac{2}{5} = \frac{8}{5} \\ \frac{8}{5} = \frac{8}{5} \\ \\ product \: of \: zeroes = \alpha \beta = \frac{c}{a} \\ \alpha \beta = \frac{ - 4}{ 5} \\ 2 \times \frac{ - 2}{5} = \frac{ - 4}{5} \\ \frac{ - 4}{5} = \frac{ - 4}{5}$

Step-by-step explanation:

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