Use the discriminant to determine the number of real roots the equation has.
7x2 + 3x + 1 =0
A. One real root (a double root)
B. Two distinct real roots
C. Three real roots
D. None (two imaginary roots)
Formula for discriminant:
d = b^2 - 4ac
note that if
d = 0 : real, equal/double root
d < 1 : imaginary roots
d > 1 : real, unequal roots
7x2 + 3x + 1 = 0
d = 3^2 - 4(7)(1)
d = 9 - 28
d = -19
Thus, it's D. imaginary roots.
Hope this helps~ :3
thank u
To determine the number of real roots the equation has using the discriminant, we need to use the following formula:
Discriminant (D) = b^2 - 4ac
where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, the equation given is 7x^2 + 3x + 1 = 0, so the coefficients are:
a = 7
b = 3
c = 1
Now, we can plug these values into the discriminant formula:
D = (3)^2 - 4(7)(1)
= 9 - 28
= -19
The discriminant is -19. Since D is negative, it means that the equation has none (two imaginary) roots. Therefore, the correct answer is:
D. None (two imaginary roots)