Question

What is the nature of roots of x- 9x = 20 ?

a. nonreal
b. real, rational, and equal
c. real, rational, and unequal
d. real, irrational, and unequal

Answer 1

Option C

Explanation:

To find the nature of the roots we use the Discriminant formula which is:

`D=b^2-4ac`

and given the equation and compare with the standard quadratic equation

`x^2-9x=20\\x^2-9x-20=0\\ax^2+bx+c=0`

Here our a is 1 , b is -9 and c is -20 so we plug a, b, c into the Discriminant formula

`D=b^2-4ac\\D=(-9)^2-4(1)(-20)\\D=81+80\\D=161`

Since D > 0 (greater than zero) our roots are real and unequal for the rational and irrational part we got know the the Discriminant's square root value if it is in decimals the nature of the roots are irrational if the Discriminant's value is a whole number then it is rational and so 161 has a square roots in points which is

`D=√(161) \\D=12.6885`

So our answer is real , irrational and unequal which is Option C