Question

for the polynomial p(x) =1/2x^2-3x+2 find the difference of zeroes

Answer 1

Hey!!!...here is ur answer

p (x)=1/2x^2-3x+2

let the zeroes are a and b

a+b=3/1/2=6
ab=2/1/2=4

difference of zeroes....
(a-b)^2=(a+b)^2-4ab
=36-4×4
=36-16
=20

a-b=root 20

Hope it will help you

Answer 2

Concept

For a polynomial, there may be some values of the variable for which the polynomial will be zero. These values are called the zeros of the polynomial.

The sum of the zeros of a quadratic polynomial is equal to the negative of the coefficient of x times the coefficient of x^2. The product of zeros is equal to the constant term by the coefficient x^2

Given

The polynomial p(x) =1/2x^2-3x+2 is given

Find

We need to find the difference of zeroes

Solution

Let the two zeroes of the polynomial be A and B

p(x) = 1/2x^2 - 3x + 2

A + B = - (Coefficient of x) / (Coefficient of x^2)

= -(-3)/(1/2) = 6

A + B = 6

AB = Constant term/ (Coefficient of x^2)

AB = 2/(1/2)

AB=4

Difference of Zeroes

=A-B

=√(A-B)^2

=√(A+B)^2 -4AB

=√(6^2 -4(4))

=√(36-16)

=√20

=2√5

Hence the difference of zeroes is 2√5

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