Question

Find the zeroes of the following polynomial 5x square-4-8x and verify the relationship between zeroes of the polynomial and the coefficients of the polynomial

Answer 1

Hey!

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5 x^2 - 4 -8x

5x^2 - 8x - 4

Where,

a = 5
b = -8
c = -4

5x^2 - 10x + 2x - 4

(5x^2 - 10x ) + (2x - 4)

5x ( x - 2) + 2 (x - 2)

= (5x + 2) ( x -2)

Zeroes are =>

5x + 2 = 0
5x = -2
x = -2/5

x -2 = 0
x = 2

Now, we know,

Sum of zeroes = - b/a

-2/5 + 2 = 8/5

8/5 = 8/5

Product of zeroes = c/a

- 2/5 × 2 = -4 /5

-4/5 = -4/5

Hence relation between the zeroes and coefficients is verified.

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Hope it helps...!!!

Answer 2

Hey dear !!!

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==> In the equation ,

5x² - 4 - 8x

By arranging we get ,

p(x) = 5x² - 8x - 4

We have to find the zeroes of this given polynomial .

Also we have,

a = 5
b = -8
c = -4

By using splitting the middle term we get ,

=> 5x² - 8x - 4

=> 5x² -10x + 2x - 4

=> 5x(x - 2) +2(x - 2)

=> (x - 2) ( 5x + 2)

If (x - 2) = 0

∴ x = 2

If (5x + 2) = 0

∴ 5x = -2

∴ x = -2/5

Therefore, 2 and -2/5 are the zeroes of the given polynomial .

Now,relation between the zeroes and the coefficient .

Let, α = 2 and β = -2/5

We know that,

α + β = -b/a

2 + (-2/5 ) = -8/5 = -b/a

Also,

αβ = c/a

2*(-2/5) = -4/5 = -b/a


Hence, the relation between the zeroes and the coefficient verified .


Thanks !!!!

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