If the roots of the equation x^2 + px + q = 0 are equal, what is the relationshi
Practice Questions
Q1
If the roots of the 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 equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
Correct Answer: p^2 = 4q
Step 1: Understand that the equation x^2 + px + q = 0 is a quadratic equation.
Step 2: Recall that a quadratic equation has equal roots when its discriminant is zero.
Step 3: The discriminant (D) for the equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
Step 4: In our equation, a = 1, b = p, and c = q. So, the discriminant becomes D = p^2 - 4(1)(q).
Step 5: Simplify the discriminant to D = p^2 - 4q.
Step 6: For the roots to be equal, 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 p and q relate to the nature of the roots of the quadratic equation.
