Question

If 1/2 is a root of the quadratic equation x2-mx5/4=0, then find the value of m​

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,

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

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

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

Taking LCM

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

cross multiplying

[tex]\implies\rm{-2 m - 4 = 0} [/tex]

[tex] \implies\rm{m=\frac{4}{-2}=-2} [/tex]

therefore,

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

Answer 2

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,

[tex]\implies\rm{x^2-mx-\frac{5}{4}=0} [/tex]

[tex] \implies\rm{{(\frac{1}{2})}^2-m(\frac{1}{2})-\frac{5}{4}=0} [/tex]

[tex] \implies\rm{\frac{1}{4}-\frac{m}{2}-\frac{5}{4}=0} [/tex]

Taking LCM

[tex] \implies\rm{\frac{1-2m-5}{4}=0} [/tex]

cross multiplying

[tex] \implies\rm{-2 m - 4 = 0} [/tex]

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

therefore,

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