To find the quadratic equation, we can use the fact that the sum of the roots is equal to the negation of the coefficient of the linear term and the product of the roots is equal to the constant term.
Let's call the roots of the quadratic equation a and b.
According to the given information:
a + b = 5 ------(1)
ab = 4 ------(2)
We can solve these equations to find the values of a and b.
From equation (1), we can express a in terms of b:
a = 5 - b
Substituting this into equation (2), we get:
(5 - b)b = 4
5b - b^2 = 4
b^2 - 5b + 4 = 0
Now, we have a quadratic equation in terms of b. We can factorize it to find the values of b.
(b - 1)(b - 4) = 0
So, b = 1 or b = 4
If b = 1, substitute this value back into equation (1) to find a:
a + 1 = 5
a = 4
If b = 4, substitute this value back into equation (1) to find a:
a + 4 = 5
a = 1
Therefore, the roots of the quadratic equation are 4 and 1.
The quadratic equation with roots 4 and 1 can be expressed as:
(x - 4)(x - 1) = 0
x^2 - 5x + 4 = 0
Therefore, the quadratic equation is option C: 2x^2 - 8x + 5 = 0.
The sum of the roots of a
quadratic equation is 5 and the product of its roots is 4. The
quadratic equation is____
A. 2x2
+ 5x + 8 = 0
B. 2x2 — 5x + 8 = 0
C. 2x2 — 8x + 5 = 0
D. 2x2
+ 8x — 5 = 0
1 answer
1 answer