Use the discriminant to determine how many real-number solutions the equation has 1 - 7a2 = -7a - 2
A) 2
B) 1
C) 0
Not sure how to work this problem
rearrange it.
7a^2+7a+2=0
discriminate= 49-4*7*2= negative number, no real solutions.
First arrange the terms in the standard form of a quadratic:
1 - 7a2 = -7a - 2
7a²-7a-3=0
The variable is a, and the coefficients of the a², a and constant terms are respectively
A=7, B=-7, C=-3
The discriminant is the expressino
D=(B²-4AC)
and the roots of the equation are:
X1,X2= (-B±√(B²-4AC))/2A
Therefore
if D>0, there are two roots, if D=0, there is one root (actually two coincident roots), and if D<0, the roots are complex, or generally considered "no root".
Post your answer for checking if you wish.
Rewrite your equation in standard form:
7a^2 -7a -3 = 0
They are trying to confuse you by using a as a variable. Think of your equation as
7x^2 -7x -3 = 0
It does not matter what symbol you giove to the unknown variable; just don't call it "a".
The numbers a, b, and c in the equation are 7, -7 and -3.
The discriminant is b^2 -4ac = 49+84 = -133
Since it is positive, there are two real solutions.
They are
x = (1/14)(7 +/- sqrt(133)]= 1.324 and
-0.324
Thanks for the Explaning this problem drwls. Ok, the first time I worked the problem I got 0 then I reworked it and got 1
-133 should be 133 in my previous answer.
There is NOT one root. There are two, if I did the numbers right.
Ok, I got it. Sorry been having problems w/ this site.Thanks I got more..
To determine how many real-number solutions the equation has, we can use the discriminant. The discriminant is a term used in quadratic equations and is defined as the expression inside the square root in the quadratic formula.
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable. In this case, the equation is given as 1 - 7a^2 = -7a - 2, so we rearrange it to the form ax^2 + bx + c = 0.
Substituting the given equation into the standard form, we have 7a^2 - 7a - 3 = 0.
Now, let's find the discriminant, denoted by the symbol Δ (delta). The discriminant is calculated using the formula Δ = b^2 - 4ac. In this equation, a = 7, b = -7, and c = -3.
Plugging in the values, we get:
Δ = (-7)^2 - 4(7)(-3)
= 49 + 84
= 133
Now, based on the value of the discriminant, we can determine the number of real-number solutions:
- If Δ > 0, the equation has two distinct real solutions.
- If Δ = 0, the equation has one real solution.
- If Δ < 0, the equation has no real solutions.
In this case, since Δ = 133, which is greater than 0, the equation has two distinct real solutions.
Therefore, the answer is A) 2.