Question

determine the nature of the root for x^2 - X - 20=0​

Answer 1

Answer :

Real and unequal roots

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 equation,

 x² - x - 20 = 0

It is of the form ax² + bx + c = 0

a = 1 , b = -1 , c = -20

Nature of roots is defined by the value of the Determinant.

D = b² - 4ac

D = (-1)² - 4(1)(-20)

D = 1 + 80

D = 81

D > 0

Hence, the roots are real and unequal.

Answer 2

formula is triangle=b²-4ac