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algebra 1 - Discriminant

by Jessica
(Lowell, IN)











































Use the discriminant to determine the nature of the roots of 4x2 + 15x + 10 = 0.

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Mar 03, 2011
Algebra 1 - Discriminant
by: Staff


The question:

by Jessica
(Lowell, IN)

Use the discriminant to determine the nature of the roots of 4x2 + 15x + 10 = 0.



The answer:


The symbol for the discriminant of a polynomial function is often represented by the Greek letter DELTA, Δ.

To type Δ on your keyboard, hold down the ALT key and type 916. Then release the ALT key.

4x² + 15x + 10 = 0

Using the quadratic formula, the roots to a quadratic equation are:

ax² + bx + c = 0

x = [-b ± sqrt(b² - 4ac)]/2a

The discriminant is the portion of the formula which is the square root:

Δ = b² - 4ac

Using the quadratic formula, the roots to your quadratic equation are:

4x² + 15x + 10 = 0

x = [-15 ± sqrt(15² - 4*4*10)]/(2*4)

The discriminant for your equation is:

Δ = 15² - 4*4*10

Δ = 65

The DISCRIMINANT is a POSITIVE number.

A positive discriminant means that the equation will have two real roots.

The final answer is: The equation will have two real roots.


Thanks for writing.


Staff
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