Question

a phone root of equation for x power 2 - 2 X + K - 4 is equal to zero is reciprocal of other then value of k is​

Answer 1

Answer :

k = 5

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

Solution :

Here ,

The given quadratic equation is ;

x² - 2x + (k - 4) = 0 .

Comparing the given quadratic equation with the general quadratic equation

ax² + bx + c = 0 , we have ;

a = 1

b = -2

c = k - 4

Also ,

It is given that , one of the root of given quadratic equation is the reciprocal of the other .

Thus ,

Let α and 1/α be the zeros of the given quadratic equation .

Now ,

=> Product of roots = c/a

=> α × 1/α = (k - 4)/1

=> 1 = k - 4

=> k = 1 + 4

=> k = 5

Hence , k = 5 .