Question

if the root of the given quadratic equation are real and equal then find the value of 'k' x²+2x+k=0​

Answer 1

Step-by-step explanation:

Both the roots of quadratic equation x^2-2.x+k = 0. , thus D or, b^2-4ac = 0.

Here , a=1. , b=-2 and c =k.

b^2 -4.a.c = 0

or, (-2)^2 -4.1.k = 0.

or, 4 = 4.k => k=4/4 = 1. Answer.

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Answer 2

Given:

A quadratic equation x² + 2x + k = 0​ has equal roots.

To Find:

The value of k such that the equation has equal roots is?

Solution:

The given problem can be solved using the concepts of quadratic equations.    

1. The given quadratic equation is   x² + 2x + k = 0.  

2. For an equation to have equal roots the value of the discriminant is 0,  

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,  

=> Discriminant ( D ) = $\sqrt{b^2-4ac}$.  

=> For equal roots D = 0.  

3. Substitute the values in the above formula,  

=>  D = 0,  

=> √[(2)²-4*1*k] = 0,

=> 4 - 4k = 0,

=> 4 = 4k,

=> k = 4/4,

=> k = 1.

Therefore, the value of k is 1.