Question

The equation $x^2 + kx + 9 = 0$ has two equal roots, then the value of k is

• A. ±6
• B. ±3
• C. ±0
• D. ±9

Answer 1

Answer:

A. ±6

For a quadratic equation of the form $ax^2 + bx + c = 0$ to have two equal roots, its discriminant ($D$) must be equal to zero:
$D = b^2 - 4ac = 0$

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Step 1: Identify the coefficients
From the given equation $x^2 + kx + 9 = 0$:

• $a = 1$

• $b = k$

• $c = 9$

Step 2: Substitute values into the discriminant formula
$k^2 - 4(1)(9) = 0$
$k^2 - 36 = 0$

Step 3: Solve for $k$
$k^2 = 36$
$k = \pm\sqrt{36}$
$k = \pm 6$

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Final Answer

The value of $k$ is $\pm 6$ (either $+6$ or $-6$).