Question

6 x2 - 3 - 7 x Find the zeroes of the following quadratic polynomial and verify the relationsp between the zeroes and the coefficient

Answer 1

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Answer 2

Hey dear !!!

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==> In the equation,

6x² - 3 - 7x

by arranging it we will get,

p(x) = 6x² - 7x - 3

We have to find the zeroes of the given polynomial, and also have to verify the relationship between the zeroes and the coefficient .

By splitting the middle term we get,

=> 6x² - 7x - 3

=> 6x² - 9x + 2x - 3

=> 6x² + 2x - 9x - 3

=> 2x(3x + 1) -3(3x + 1)

=> (3x + 1) (2x - 3)

If (3x + 1) = 0

∴ 3x + 1 = 0

∴ 3x = -1

∴ x = -1/3 is our first zeros

similarly ,

If (2x - 3) = 0

∴ 2x - 3 = 0

∴ 2x = 3

∴ x = 3/2 is our second zeros

[Therefore, -1/3 and 3/2 are the zeroes of the given polynomial . ]

Now, relation between the zeros and the coefficient .

Let α = -1/3 and β = 3/2

We also have ,

a = 6

b = -7

c = -3

We know that,

α + β = -b/a

-1/3 + 3/2 = -(-7/6) = -b/a

And,

αβ = c/a

-1/3*3/2 = -3/6 = c/a

Thanks !!!