Question

find zeroes of quadratic polynomial and find the relation hip between the zeroes and the coefficients 1.x2-2x-8​

Answer 1

S O L U T I O N :

⠀ ⠀

We're given with a polynomial that is x² – 2x – 8. And, we're asked to find the zeroes of this given polynomial and verify the relationship b/w the zeroes and the coefficients of the polynomial. Firstly, we'll find out the zeroes of the polynomial by using the method given below.

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• S P L I T T I N G⠀T H E⠀M I D D L E⠀T E R M :

↠ x² – 2x – 8 = 0

↠ x² – 4x + 2x – 8 = 0

↠ x(x – 4) + 2(x – 4) = 0

↠ (x – 4) (x + 2) = 0

↠ x = 4 & – 2

∴ Therefore, the zeroes of the polynomial are α = 4 and β = – 2 respectively.

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★ On Comparing with the Quadratic polynomial (ax² + bx + c = 0) —

• a = 1
• b = – 2
• c = – 8

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★ V E R I F I C A T I O N $:$

For any Quadratic polynomial the sum and product of the roots are Given by :

• (α + β) = –b/a
• (αβ) = c/a

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S U M⠀O F⠀Z E R O E S :

➟ α + β = –b/a

➟ 4 + (– 2) = – (– 2)/1

➟ 2 = 2

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P R O D U C T⠀O F⠀Z E R O E S :

➟ αβ = c/a

➟ (4) (– 2) = – 8/1

➟ – 8 = – 8

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⠀ ⠀ ⠀⠀⠀⠀ ∴ Hence, Verified!

Answer 2

x^2 - 2x - 8

X^2 -4x + 2x - 8

x(x - 4) + 2 ( x - 4 )

( x + 2 ) ( x - 4 )

X = -2 or 4

Hence zeroes are -2 and 4

Verification:

A = 1

B= -2

C = -8

Alpha + Beta = -b/a

-2 + 4 = -(-2)/1

2 = 2

Alpha Beta = c /a

-2 (4) = -8/1

-8 = - 8

Hence Verified