The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":
<span>Δ=<span>b2</span>−4ac</span>
Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios:
<span>if→Δ>0<span>=></span>∃<span>x1</span>,<span>x2</span>/a<span>x2</span>+bx+c=0</span>
This just means: "if the discriminant is greater than zero, there will exist two x-intercepts"
And for the second scenario:
<span>if→Δ=0→∃<span>xo</span>/a<span>x2</span>+bx+c=0</span>
This means: "if the discriminant is equal to zero, there will be one and only one x-intercept"
And for the last scenario:
<span>if→Δ<0→∃x∉R/a<span>x2</span>+bx+c=0</span>
This means that :"if the discriminant is less than zero, there will be no x-intercepts"
So, if we take your excercise and analyze the the discriminant:
<span>3<span>x2</span>+7x+m=y</span>
we will find the values that satisfy y=0 :
<span>3<span>x2</span>+7x+m=0</span>
And we'll analyze the discriminant:
<span>Δ=<span>72</span>−4(3)(m)</span>
And we are only interested in the values that make the discriminant equal zero:
<span><span>72</span>−4(3)(m)=0</span>
All you have to do is solve for "m".
Gas is $2.53⁹ per gallon today, at that filling station
down the street from my house.
I have $10 in my pocket.
a). How much gas can I put in the car if I go there ?
b). My car gets 25 miles per gallon. How many 'miles' will my $10 buy ?
c). In Calgary (Alberta, Canada) today, gas is selling for
89¢ (Canadian) per liter. What is the percentage more or less,
compared to the price of gas down the street from my house ?
If I posted this problem on Brainly, I'd probably give it
something like 5 points for part-a, another 5 for part-b,
and 10 or 15 for part-c because in addition to math,
that part takes some research.
Answer:
x= 36
Step-by-step explanation:
0.2(3x+2)+4=26
0.6x+0.4+4=26
0.6x+4.4=26
0.6x=21.6
x=36