Question

For what value of 'k' will the following quadratic equation :
(k+1)x^2 - 4kx + 9 = 0 have real and equal roots ? Solve the equation

Answer 1

Answer:

K = 3, -3/4

if k=3

then a= 3/2 ,3/2

if K=-3/4

then a= -6,-6

Answer 2

The value of k is -3/4 or 3.

Given,

A quadratic equation (k+1)x²- 4kx+9 = 0.

To Find,

The value of k such that the given equation has equal roots.

Solution,

For a quadratic equation to have real and equal roots, the value of its discriminant must be equal to 0.

So,

D = 0

The formula for calculating D is √(b²-4ac)

So,

√(b²-4ac) = 0

(4k)²-4(k+1)(9) = 0

4k²-9k-9 = 0

Solving this quadratic equation using the middle term splitting method,

4k(k-3)+3(k-3) = 0

(4k+3)(k-3) = 0

k = -3/4 or 3

Hence, the value of k is -3/4 or 3.

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