Question

Find the nature of roots of the quadratic equation 2x^-4x+3=0
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given: $\sf 2x^2\ -\ 4x\ +\ 3\ =\ 0.$

To find: The nature of the roots (D).

Answer:

Discriminants (D) tell us if the equations has roots or not.

$\sf D\ =\ b^2\ -\ 4 ac$

Conditions to determine the nature of the roots:

• If  $\sf b^2\ -\ 4ac$  =  0, the equation has real roots.
• If  $\sf b^2\ -\ 4ac$  <  0, the equation has no real roots.
• If  $\sf b^2\ -\ 4ac$  >  0, the equation has real and distinct roots.

$\sf 2x^2\ -\ 4x\ +\ 3\ =\ 0\\\\From\ this\ equation,\ \\\\a\ =\ 2\\b\ =\ -\ 4\\c\ =\ 3\\\\\\b^2\ -\ 4ac\ \\\\\implies\ (-4)^2\ -\ 4(2)(3)\\\\=\ 16\ -\ 24\\\\=\ -8$

Since - 8 is lesser than zero, the equation has no real roots.