Question

What is the discriminant of x^2-4x=9

Answer 1

Discriminant is -20 (D<0, no real roots)

Explanation:

The Discriminant Formula:

`\displaystyle \large{ D = {b}^(2) - 4ac}`

First, arrange expression in the standard form or ax^2+bx+c = 0.

`\displaystyle \large{ {x}^(2) - 4x = 9} \\ \displaystyle \large{ {x}^(2) - 4x - 9 = 0}`

From above, we subtract both sides by 9.

Compare the coefficients:

`\displaystyle \large{a {x}^(2) + bx + c = {x}^(2) - 4x - 9}`

• a = 1
• b = -4
• c = -9

Substitute a = 1, b = -4 and c = -9 in the formula.

`\displaystyle \large{ D = {( - 4)}^(2) - 4(1)( - 9)} \\ \displaystyle \large{ D = 16 - 4( - 9)} \\ \displaystyle \large{ D = 16 - 36} \\ \displaystyle \large{ D = - 20}`

Therefore the discriminant of equation is -20 which is less than 0.