If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the r
Practice Questions
Q1
If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
p^2 = 4q
p^2 > 4q
p^2 < 4q
p + q = 0
Questions & Step-by-Step Solutions
If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
Step 1: Understand that a quadratic equation is in the form x^2 + px + q = 0.
Step 2: Identify that the roots of the equation are the values of x that make the equation true.
Step 3: Recognize that for the roots to be equal, a specific condition must be met regarding the discriminant.
Step 4: The discriminant (D) of a quadratic equation is calculated using the formula D = p^2 - 4q.
Step 5: For the roots to be equal, the discriminant must be zero (D = 0).
Step 6: Set the discriminant equal to zero: p^2 - 4q = 0.
Step 7: Rearrange the equation to find the relationship between p and q: p^2 = 4q.
Discriminant of a Quadratic Equation – The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. For the roots to be equal, D must equal zero.
Relationship Between Coefficients – Understanding how the coefficients of a quadratic equation relate to the nature of its roots, particularly when they are equal.
