Question

If the sum and difference of zeroes of quadratic polynomial are -3 and -10 then find the difference of the squares of zeroes

Answer 1

Answer:  The difference of the squares of zeroes is 30

Step-by-step explanation

      α + β = -3 --1)

      α - β  =  -10 --2)

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       2α    =  -13

         α    =   -13/2

Substitute α= -13/2 in Eq 1

α + β = -3

-13/2 + β = -3

      β   =  -3 + 13/2

      β   =   7/2

α = -13/2 and β = 7/2

therefore,   the difference of the squares of zeroes

$\alpha ^{2} - \beta ^{2}$

= $(-13/2)^{2} - (7/2)^{2}$

=   169/4  -  49/4

=   120/4

= 30

Hope this helps!!

Cheers!!