Question

If alpha and beta are the zeros of the given polynomial p(x)= x^2-x-4 then find the value of 1/alpha + 1/beta - alpha*beta

Answer 1

P(x) = x²-x-4

Sum of zereos =-b/a

Alpha + beta = -(-1/1)=1

Product of zereos=c/a

Alpha*beta= -4

1/alpha +1/ beta ( taking lcm)

Alpha + beta / alpha*beta

1/-4= -1/4

So -1/4 is the answer

Answer 2

Answer:

The value of ( 1 / α ) + ( 1 / β ) - αβ is 15 / 4.

Step-by-step-explanation:

The given quadratic polynomial is x² - x - 4.

We have given that,

α and β are the zeros of quadratic polynomial.

Comparing the quadratic polynomial with ax² + bx + c, we get,

• a = 1
• b = - 1
• c = - 4

We know that,

Sum of zeros = - b / a

⇒ α + β = - ( - 1 ) / 1

⇒ α + β = 1

And,

Product of zeros = c / a

⇒ αβ = - 4 / 1

⇒ αβ = - 4

Now,

( 1 / α ) + ( 1 / β ) - αβ = [ ( α + β ) / αβ ] - αβ

⇒ ( 1 / α ) + ( 1 / β ) - αβ = ( 1 / - 4 ) - ( - 4 )

⇒ ( 1 / α ) + ( 1 / β ) - αβ = ( - 1 / 4 ) + 4

⇒ ( 1 / α ) + ( 1 / β ) - αβ = ( - 1 + 16 ) / 4

⇒ ( 1 / α ) + ( 1 / β ) - αβ = 15 / 4

∴ The value of ( 1 / α ) + ( 1 / β ) - αβ is 15 / 4.