How do you find the value of the discriminant and determine the nature of the roots $8x^2 – 2x – 18 = -15$ ?

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Answer 1 · 2016-09-04T17:10:17

The discriminant of the second degree equation $ax^2+bx+c=0$ is:
$b^2-4*a*c$

and the solutions depend on whether the two values $+- sqrt(b^2-4*a*c)$ , are real or not

The given equation in the standard form $ax^2+bx+c=0$ is $8x^2-2x-3=0$

Then, $+- sqrt(b^2-4*a*c)$ in our case is $+- sqrt((-2)^2-4*(8)*(-3))=+-sqrt(100)=+-10$ .

the value of the discriminant is 100, so the two values of the square root are real, and there are two real solutions to the equation.

Answer 2 · 2016-09-04T17:15:08

There are 2 real roots which are irrational and distinct (different)

Make the quadratic equation = 0.

$8x^2 -2x-3 = 0 larr$ this is in the form $ax^2 +bx + c = 0$

The discriminant is given by $Delta = b^2 - 4ac$

$Delta = (-3)^2 - 4(8)(-3) = 9+96 = 105$

What does this value of 105 tell us?

$Delta > 0 rarr$ there are 2 distinct (different) real roots.

$Delta = 105$ which is not a perfect square
$rarr$ the roots are irrational.

There are 2 real roots which are irrational and distinct (different)

How do you find the value of the discriminant and determine the nature of the roots 8x^2 – 2x – 18 = -15 8x^2 – 2x – 18 = -15 ?