Question

If α and β αre zeros of Quadratic polynomial p(x) = x² +10x+25 Find the value of (α+β)/αβ.

​

Answer 1

Answer :

The value of (α + β)/αβ is -2/5

Step-by-step explanation :

➤ Quadratic Polynomials :

✯ It is a polynomial of degree 2

✯ General form :

      ax² + bx + c  = 0

✯ Determinant, D = b² - 4ac

✯ Based on the value of Determinant, we can define the nature of roots.

    D > 0 ; real and unequal roots

    D = 0 ; real and equal roots

    D < 0 ; no real roots i.e., imaginary

✯ Relationship between zeroes and coefficients :

     ✩ Sum of zeroes = -b/a

     ✩ Product of zeroes = c/a

________________________________

Given quadratic polynomial,

p(x) = x² + 10x + 25

It is of the form ax² + bx + c

a = 1 , b = 10 , c = 25

⇒ Sum of zeroes = -b/a

   α + β = -10/1

   α + β = -10

⇒ Product of zeroes = c/a

    αβ = 25/1

    αβ = 25

(α + β)/αβ = ?

(α + β)/αβ = -10/25

(α + β)/αβ = -2/5

The value of (α + β)/αβ is -2/5

Answer 2

$\huge\sf\underline\blue{Refer to attachment}$