Question

Find the zero of the polynomial and verify the relationship between zero and the coefficent of zero

5x^2-8x-4​

Answer 1

Given :-

• 5x² - 8x - 4

To find :-

• The zero of the polynomial and verify the relationship between zero and the coefficent of zero.

Solution :-

→ 5x² - 8x - 4

• Split middle term

→ 5x² - 10x + 2x - 4

→ 5x(x - 2) + 2(x - 2)

→ (x - 2)(5x + 2)

Either

→ x - 2 = 0

→ x = 2

Or

→ 5x + 2 = 0

→ 5x = - 2

→ x = -2/5

Verification

• Sum of zeros

→ 2 + (-2)/5 = 2 - 2/5 = 8/5 = -(coefficient of x)/coefficient of x²

• Product of zeros

→ 2 × (-2)/5 = - 4/5 = constant term/coefficient of x²

• Hence verified

Answer 2

$\sf\green{\ast}\underline{\red{Question}} \green{\ast}$

Find the zero of the polynomial and verify the relationship between zero and the coefficent of zero:-

5x^2-8x-4

$\sf\pink{\ast}\underline{\blue{Solution}} \pink{\ast}$

ɢɪᴠᴇɴ:-

p(x)=0

→5x²-8x-4=0

ᴛᴏ ғɪɴᴅ:-

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

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

→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

$\sf\blue{↬}$5x+2=0

$\sf\orange{↬}$x-2=0

_______________________________

$\sf\purple{↬}$Taking x-2,

→x-2=0

x=2→(α)

_______________________________

$\sf\pink{↬}$Taking 5x+2

→5x+2=0

→5x=-2

x=$\frac{-2}{5}$→(β)

_______________________________

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

→α+β=$\frac{-b}{a}$

→2+(-⅖)=$\frac{-(-8)}{5}$

[Cross Multiply, LHS]

→$\frac{10-2}{5}$=$\frac{8}{5}$

→$\frac{8}{5}$=$\frac{8}{5}$

Ꮩerified

_______________________________

αβ=$\frac{c}{a}$

2×(-⅖)=$\frac{-4}{5}$

→-⅘=-⅘

Ꮩerified

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