Question

If ½ is a root of the quadratic equation x2-mx-5/4=0, then value of m is​

Answer 1

Solution :-

∵ 1/2 is a root of quadratic eqn

x²-mx-5/4 = 0

∴ on putting x = 1 / 2, x² - m x - 5/4 should equate with zero

so,

$\implies\rm{x^2-mx-\frac{5}{4}=0}$

$\implies\rm{{(\frac{1}{2})}^2-m(\frac{1}{2})-\frac{5}{4}=0}$

$\implies\rm{\frac{1}{4}-\frac{m}{2}-\frac{5}{4}=0}$

Taking LCM

$\implies\rm{\frac{1-2m-5}{4}=0}$

cross multiplying

$\implies\rm{-2 m - 4 = 0}$

$\implies\rm{m=\frac{4}{-2}=-2}$

therefore,

$\boxed{\boxed{\red{\bf{m=-2}}}}$

Answer 2

Given:

1/2 is a root of a quadratic equation x² - m x -5/4 = 0.

To Find:

The value of m is?

Solution:

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

1. The roots of a quadratic equation are defined as the values of x such that when substituted the value of the equation becomes 0.

2. There can be a maximum of 2 roots in a quadratic equation. The roots can be either 1 or 0 also.

2. As 1/2 is a root of the given quadratic equation. The value when substituted in the equation must be equal to 0.

=> x² - m x -5/4 = 0,

=> (1/2)² - m(1/2) -5/4 = 0,

=> 1/4 -(m/2) -5/4 = 0,

=> m/2 = 5/4 - 1/4,

=> m/2 = (4/4),

=> m/2 = 1,

=> m = 2.

Therefore, the value of m is 2.