For what value of k the quadratic equation x²-kx+4=0 has equal roots?

Question

Answer

X^2-kx+4=0
for having equal roots
b^2-4AC=0
(-k)^2-4(1)(4)=0
k^2-16=0
k=4or-4

Answer

X²-kx+4a=1b=-kc=4
D=0b²-4ac=0K²-4(1)(4)=0K²-16=0K=+4,-4

Answer

A+B=-k..
2a=-k..
a=-k/2 ... (1)...

also,a×b=4..
a^2=4 ...

a=+,- 2 ... (2)...

from eqn (1) &(2) ..

k=4 or (-4). ..

Answer

I think you're question has mistake

Answer

Introduction:

To find the value of k for which the quadratic equation x² - kx + 4 = 0 has equal roots, we need to determine the discriminant of the equation. The discriminant is the term under the square root in the quadratic formula and it helps us determine the nature of the roots.

Quadratic Equation:

The given quadratic equation is x² - kx + 4 = 0.

Determining the Discriminant:

The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula D = b² - 4ac.

In our equation x² - kx + 4 = 0, a = 1, b = -k, and c = 4. Substituting these values into the discriminant formula, we get D = (-k)² - 4(1)(4).

Simplifying further, D = k² - 16.

Conditions for Equal Roots:

For a quadratic equation to have equal roots, the discriminant must be equal to zero. So, we need to solve the equation k² - 16 = 0.

Solving for k:

To find the value of k, we can solve the equation k² - 16 = 0.

Taking the square root of both sides, we have √(k² - 16) = √0.

Simplifying further, we get k = ±√16.

Therefore, k = ±4.

Conclusion:

The value of k for which the quadratic equation x² - kx + 4 = 0 has equal roots is k = ±4.

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