For the following equation, state the value of the discriminant and then describe the nature of the solutions.
-15x² + 2x + 13 = 0
What is the value of the discriminant?
Using the conventional formula
ax^2 + bx + c for the quadratic polynomial, the discriminant is b^2 -4ac.
In this case, that equals 4 - (-780)= 784. The discriminant is positive. There are two roots and both are real. The square root of the discriminant is 28.
The roots are (-1/30)(-2 +/-28)
= 1 and -13/15
To find the value of the discriminant for the given equation -15x² + 2x + 13 = 0, we can use the formula for the discriminant, which is b² - 4ac.
The coefficients of the equation are:
a = -15
b = 2
c = 13
Substituting these values into the formula, we have:
discriminant = b² - 4ac
= (2)² - 4(-15)(13)
= 4 + 780
= 784
Therefore, the value of the discriminant for the given equation is 784.