find the value of the discriminant: Use that number to describe the nature of the roots:
a. 12x^2+2x+5=0
b. x^2+6x=0
2: suppose f(x)=3x^2+2x1
a. find x if f(x)=7
b. find the x-intercepts
c. find f(-4)
d.find (2)
for $\displaystyle ax^2+bx+c=0 $ the discriminant is $\displaystyle \Delta = b^2-4ac$
When
$\displaystyle \Delta >0$ your quadratic has two distinct real roots
$\displaystyle \Delta =0$ your quadratic has one repeated real root
$\displaystyle \Delta <0$ your quadratic has no real roots
for $\displaystyle 12x^2+2x+5=0$ then $\displaystyle a = 12, b=2$ and $\displaystyle c = 5$
so $\displaystyle \Delta = 2^2-4\times 12 \times 5 = \dots$
finish this and make your conclusion.
Do you know that the discriminant of $\displaystyle ax^2+ bx+ c= 0$ is $\displaystyle b^2- 4ac$.
was this supposed to be "+ 1"? I will assume f(x)= 3x^2+ 2x+ 1.2: suppose f(x)=3x^2+2x1
Solve 3x^2+ 2x+ 1= 7a. find x if f(x)=7
Those are where f(x)= 0. Solve 3x^2+ 2x+ 1= 0.b. find the x-intercepts
That is just 3(-4)^2+ 2(-4)+ 1.c. find f(-4)
Assuming you mean f(2), it is just 3(2)^2+ 2(2)+ 1.d.find (2)