Question

Obtain quadratic equation if roots are 2-root 5 and 2 +root 5

Answer 1

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Step-by-step explanation:

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Answer 2

Answer :

x² - 4x - 1

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

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Given roots of the equation are 2 - √5 and 2 + √5

⇒ Sum of roots =  2 - √5 + 2 + √5

                          =  4

⇒ Product of roots =  (2 - √5) × (2 + √5)

                               =  2(2 + √5) - √5(2 + √5)

                               =  4 + 2√5 - 2√5 - √5²

                               =  4 - 5

                               =  -1

                              

The quadratic polynomial is of the form :

x² - (sum of zeroes)x + (product of zeroes)

x² - (4)x + (-1)

x² - 4x - 1

∴ The required polynomial = x² - 4x - 1