Question

if alpha and beta are the zeros of the polynomial 5x^2 -8x-4 write the value of alpha +beta +alphabeta

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Answer 1

Answer:

For a quadratic equation, ax2+bx+c=0,

The sum of the roots=a−b and product of the roots is ac

Here sum of roots= α+β=2−5

Product of roots=αβ=21

Therefore,α+β+αβ=2−5+21

⇒ α+β+αβ=−2

Therefore,Option A is correct.

Answer 2

Solution

Given :-

• Polynomial, 5x² - 8x - 4 = 0
• α & β are roots of this Equation.

Find :-

• Value of α + β + α β

Explanation

Formula

★Sum of roots = -(coefficient of x)/(coefficient of x²)

★Product of roots = (constant part)/+coefficient of x²)

So, Now

==> Sum of roots = -(-8)/5

==> α + β = 8/5 ______________(1)

and,

==> Product of roots = (-4)/5

==> α β = -4/5________________(2)

Now , add Equation (1) & Equation (2)

==> α + β + α β = 8/5 - 4/5

==> α + β + α β = (8 - 4)/5

==> α + β + α β = 4/5

Hence

• Value of α + β + α β will be = 4/5

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