1.

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

Answer»

Given:-

<P>

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}


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