Question

Determine the discriminant for the quadratic equation 0 = –2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?
Discriminant = b2 – 4ac


real number solutions

Answer 1

we know that

In a quadratic equation of the form $ax^{2}+bx+c=0$ the discriminant is equal to

$(b^{2} -4ac)$

if  $(b^{2} -4ac)> 0$ -------> the equation has two real number solutions

if  $(b^{2} -4ac)= 0$ -------> the equation has one real number solution

if  $(b^{2} -4ac)< 0$ -------> the equation has two complex number solutions

In this problem we have

$-2x^{2} +3=0$

so

$a=-2\ b=0\ c=3$

substitute in the formula

$(0^{2} -4(-2)(3))=24$

$24 > 0$ ---->  the equation has two real number solutions

therefore

the answer is

the equation has two real number solutions

Answer 2

Determine the discriminant for the quadratic equation 0 = –2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?  Remember that the discriminant is calculated using the coefficents a, b and c.  Given 0 = -2x^2 + 0x + 3, the coeff. are a=-2, b=0 and c=3.

The discriminant is b^2 - 4ac.  Here, the discriminant is 0^2 - 4(-2)(3) = 24.

Since the discriminant is positive, you have two real, unequal roots.