Question

➡️For the polynomial p(x) = 1/2x²-3x+2; find the difference of zeroes.
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Answer 1

α and β are the zeroes of the polynomial f(x) = 2x² + 5x + k. Sum of the zeroes = α + β = -(coefficient of x) / (coefficient of x2) = -5/2. Product of the zeroes = αβ = -(constant term) / (coefficient of x2) = k/2.

hope it helps you

Answer 2

Solution :-

Given Polynomial :-

1/2x^2 - 3x + 2

Let's compare this equation with ax^2 + bx + c = 0

Then ,

a = 1 /2 , b = - 3 and c = 2

Therefore,

As we know that,

The sum of zeroes = α + β = -b/a

Put the required values,

α + β = - ( -3)/1/2

α + β = 3 * 2 / 1

α + β = 6

Now,

The product of zeroes = αβ = c/a

Put the required values,

αβ = 2/1/2

αβ = 4

Difference between the zeroes of polynomials

( a - b)^2 = ( a + b)^2 - 4ab

Put the required values,

( a - b)^2 = 36 - 4 * 4

( a - b)^2 = 36 - 16

( a - b)^2 = 20

Now,

a - b = √ 20

Hence, The difference between the zeroes of polynomials is √20 $.$