Im lost i don't know how to do this can someone show me step by step how to solve this
For what value of c does the equation have one real root? Hint using the values of a and b found in the equation, solve D = 0 for c.
Consider the quadratic expression X^2 + 4x + c = 0.
Recall the formula for discriminant. For a quadratic equation in the general form, ax^2 + bx + c = 0,
D = b^2 - 4ac
if
D = 0 : real, equal/double root
D > 0 : two real, unequal roots
D < 0 : two imaginary roots
Since we're required to have one real root, we equate D to zero, and solve for the unknown, c.
x^2 + 4x + c = 0
a = 1
b = 4
c = ?
Substituting to the discriminant formula, (D = 0)
0 = 4^2 - 4*1*c
0 = 16 - 4c
4c = 16
c = 4
Hope this helps~ :3
To find the value of c for which the quadratic equation has one real root, we need to find the discriminant (D) of the quadratic equation.
The discriminant is determined by the coefficients of the quadratic equation and is given by the formula:
D = b^2 - 4ac
In this case, the quadratic equation is X^2 + 4x + c = 0, where a = 1, b = 4, and c is the value we want to find.
To find the discriminant, we substitute the values of a, b, and c into the formula:
D = (4)^2 - 4(1)(c)
= 16 - 4c
Now, to find the value of c for which the equation has one real root, we need to set the discriminant equal to zero and solve for c:
D = 0
16 - 4c = 0
Subtracting 16 from both sides:
-4c = -16
Dividing both sides by -4:
c = 4
Therefore, the value of c for which the equation has one real root is c = 4.