Question

if alpha and beta are the zeros of the quadratic polynomial f x is equal to x square- X + 4 find the value of alpha + beta minus alpha beta

Answer 1

Hey dear
we know that sum of zeroes = alpha + beta
=- coefficient of x/ coefficient of x²
=-(-1)/1
And product of zeroes=alpha/beta
= constant/coefficient of x²
=4/1
from this( alpha + beta)- alpha beta =
1/1-4/1
=1-4=-3

May this will help u

pls mark it as brainleist

Answer 2

Hey Mate !

Here is your solution :

Given,

f(x) = x² - x + 4.

α and β be its zeroes.

Here,

Coefficient of x² ( a ) = 1

Coefficient of x ( b ) = -1

Constant term ( c ) = 4

We know the relationship between zeroes and coefficients of x.

=> Sum of zeroes = -b/a

=> α + β = -( -1 ) / 1

=> α + β = 1 -------- ( 1 )

And,

=> Product of zeroes = c/a

=> αβ = 4/1

=> αβ = 4 -------- ( 2 ).

Now,

= ( α + β ) - α β

By substituting the value of ( 1 ) and ( 2 ),

= ( 1 ) - 4

= 1 - 4

= -3

The required answer is ( -3 ).


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Hope it helps !!