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

Question

Answer

Given Quadratic Equation is x^2 - kx + 4 = 0.

Comparing Equation with ax^2 + bx + c = 0

a = 1, b = -k, c = 4.

Given that the Equation has real roots.

D = 0

b^2 - 4ac = 0

(-k)^2 - 4(1)(4) = 0

k^2 - 16 = 0

k^2 = 16

k = 4 (or) - 4.

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.

Similar Class 10 Doubts

Find the value of k if the quadratic equation 3x² - k√3 x+4=0 has equal roots?

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

If -5 is a root of the quadratic equation 2x^2 px-15=0 and the quadratic equation p(x^2 X)k=0 has equal roots. Find the value of k?

If -5 is root of the quadratic equation 2x^2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots ,then the value of k.?

If -5 is the root of the quadratic equation 2x^2 px-15=0 and the equation p(x^2 x) k=0 has a real and equal roots find the value of k?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company