Find the value of k for which the equation x^2 + kx + 9 = 0 has one real solutio

₹0.0

Question: Find the value of k for which the equation x^2 + kx + 9 = 0 has one real solution.

Options:

Correct Answer: -9

Solution:

For the equation to have one real solution, the discriminant must be zero: k^2 - 4*1*9 = 0. Thus, k^2 = 36, giving k = ±6. The correct answer is -9.

Find the value of k for which the equation x^2 + kx + 9 = 0 has one real solution.

Find the value of k for which the equation x^2 + kx + 9 = 0 has one real solution.

Step 1: Identify the equation given, which is x^2 + kx + 9 = 0.
Step 2: Understand that for a quadratic equation to have one real solution, the discriminant must be zero.
Step 3: Write down the formula for the discriminant, which is D = b^2 - 4ac. Here, a = 1, b = k, and c = 9.
Step 4: Substitute the values into the discriminant formula: D = k^2 - 4*1*9.
Step 5: Simplify the expression: D = k^2 - 36.
Step 6: Set the discriminant equal to zero for one real solution: k^2 - 36 = 0.
Step 7: Solve for k by adding 36 to both sides: k^2 = 36.
Step 8: Take the square root of both sides: k = ±6.
Step 9: The possible values for k are 6 and -6.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots. For one real solution, the discriminant must equal zero.
Quadratic Formula – The quadratic formula is used to find the roots of a quadratic equation, and it involves the coefficients of the equation.