Question

If alpha +beeta are the zeroes of the polynomial p(x)=2x^+5x+r such that alpha square+beeta square+alpha×beeta=21÷4 . Find r

Answer 1

Answer:

r = 2

Explanation: 2x² + 5x + r

We know that α+β=-b/a = -5/2

αβ = c/a = r/2

So now ,

α²+β²+αβ can be written as (α+β)²- αβ bcoz when we will open the bracket then 2αβ-αβ =αβ as given in eqn.

So now ,

(α+β)²-αβ=21/4

now putting the values,

(-5/2)²-r/2=21/4

25/4-r/2=21/4

- r/2= - 4/4

minus cancelled

r/2=1

r=2

Hope u understood !!

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