Question

find the discriminant.
$2x^{2}-2x-6=0$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Identify coefficients

For quadratic $ax^2+bx+c=0$, $a=2$, $b=-2$, $c=-6$

Step2: Apply discriminant formula

Discriminant $D=b^2-4ac$
$D=(-2)^2-4(2)(-6)$

Step3: Calculate discriminant value

$D=4 + 48 = 52$

Step4: Analyze discriminant sign

Since $D>0$, quadratic has two real roots.

Answer:

Discriminant: $52$
Number of real solutions: two real solutions