Question

X^2 -3x+18 find the discriminate

Answer 1

-63

Explanation:

\[x²-3x+18\]

discriminant=b²-4ac=(-3)²-4*1*18=9-72=-63

Answer 2

`\boxed {\boxed {\sf -63}}`

Explanation:

The discriminant is the portion of the Quadratic Formula that is under a square root. It helps us identify if a function has 2,1, or 0 solutions.

The quadratic formula is:

`{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}`

where the quadratic is: ax²+bx+c

The part under the square root is just:

`b^2-4ac}`

We are given the quadratic:

x² -3x+18

Therefore,

• a= 1 (there is an implied coefficient of 1 in front of the x²)
• b= -3
• c= 18

Substitute the values into the formula for the discriminant.

`(-3)^2-4(1)(18)}`

Solve the exponent.

• -3² = -3*-3 = 9

`9-4(1)(18)}`

Multiply.

• 4(1)(18)= 4*18=72

`9-72`

Subtract

`-63`

Since the discriminant is negative, there are no real solutions. There are imaginary solutions though.