If the roots of the equation x^2 + 5x + k = 0 are 1 and 4, what is the value of

₹0.0

Question: If the roots of the equation x^2 + 5x + k = 0 are 1 and 4, what is the value of k?

Options:

Correct Answer: 6

Solution:

Using the product of roots, k = 1*4 = 4.

If the roots of the equation x^2 + 5x + k = 0 are 1 and 4, what is the value of k?

If the roots of the equation x^2 + 5x + k = 0 are 1 and 4, what is the value of k?

Step 1: Understand that the equation x^2 + 5x + k = 0 is a quadratic equation.
Step 2: Know that the roots of the equation are given as 1 and 4.
Step 3: Recall that for a quadratic equation ax^2 + bx + c = 0, the product of the roots (r1 and r2) can be found using the formula r1 * r2 = c/a.
Step 4: In our equation, a = 1 (the coefficient of x^2) and c = k (the constant term).
Step 5: Calculate the product of the roots: 1 * 4 = 4.
Step 6: Since the product of the roots equals k (the constant term), we have k = 4.

Quadratic Equations – Understanding the relationship between the coefficients of a quadratic equation and its roots, specifically using Vieta's formulas.
Roots of Equations – Identifying and applying the properties of roots, including the sum and product of roots.