Answer:
Below in BOLD.
Step-by-step explanation:
1. The discriminant D = b^2 - 4ac
= 3^2 - 4*5*(-7)
= 9 + 140
= 149.
Positive value so it has 2 real solutions.
2. D = (-12)^2 - 4 * 9 * 4
= 144 - 144
= 0.
So it has one real solution.
3. D = 2^2 - 4*1*3
= -8.
It is negative so there are No real solutions.
4. D = 4^2 - 4*2*10 = 16 - 80 = -64.
No solutions.
5. D = (-12)^2 - 4*3*(12)
= 144 - 144 = 0
So its the second choice.
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".
means to say there is some number
for which any choice of
such that
Working backwards, we have
So, whenever
, we can always guarantee that
.
Answer:
Hey there the answer is $5.10 but if you need the full price it is $90.10
Step-by-step explanation:
Answer:
X= 2
y = 2
Step-by-step explanation:
y=-2x+6............... equation 1
y=3x-4................... equation 2
from equation 2
y=3x-4
substitute y=3x-4 in equation 1
3x-4=-2x+6
collect like terms
3x+2x=6+4
5x=10
divide both sides by 5
X=2
substitute X=2 in equation 1
y=-2x+6
y=-2(2)+6
y=-4+6
y=2
hope it helps
