The correct statements about the following quadratic equation are true ;the discriminant is greater than zero, so there are two real roots.
How to use the discriminant to find the property of solutions of given quadratic equation?
Let the quadratic equation given be of the form
[tex]ax^2 + bx + c = 0[/tex],
then
The quantity b^2 - 4ac is called its discriminant.
The solution contains the term[tex]\sqrt{b^2 - 4ac}[/tex]
which will be:
Real and distinct if the discriminant is positive
Real and equal if the discriminant is 0
Non-real and distinct roots if the discriminant is negative
[tex]6x^2 - 8 = 4x^2 + 7x\\6x^2 - 4x^2 - 7x - 8 = 0\\2x^2 - 7x - 8 = 0[/tex]
The discriminant = b^2 - 4ac;
where a = 2, b = -7 and c = -8
[tex]d = (-7)^2 - 4(2)(-8)\\d = 49 + 64\\d = 113[/tex]
Therefore, the discriminant is greater than zero, so there are two real roots.
Learn more about the discriminant of a quadratic equation here:
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