Question

Determine the value of the root of the following quadratic equation from their discriminant x² -2x+ 9/4 = 0​

Answer 1

❂ GIVEN :

• $\sf{x^2 -2x+\dfrac{9}{4} = 0}$ .

❂ TO FIND :

• The value of the root.

⚛SOLUTION:-

⦿ We have,

• a = 1
• b = -2
• c = 9/4

☦FORMULA USED :

• $\underline {\huge {\red{\bf{D= b^2 - 4ac}}}}$

Putting the values in the formula:

$: \implies \sf{D= b^2 - 4ac}$

$: \implies \sf{D= ( - 2)^2 - \cancel{4}\times 1\times \dfrac{9}{\cancel{4}} }$

$: \implies \sf{D= 4 - 9}$

$: \implies \underline{\underline{\huge{\boxed{\pink{\bf{D= -5}}}}}}$

•°• Here, we found that Discriminant < 0 so the roots are unreal and imaginary.

Answer 2

$\large\bf{\color{navy}{Correct~Question}}$

Determine the value of the root of the following quadratic equation from their discriminant $\sf{x^2 -2x+\dfrac{9}{4}= 0}$

$\large\bf{\color{orange}{Given}}$

$\sf{x^2 -2x+\dfrac{9}{4} = 0}$

$\large\bf{\purple{To~Find}}$

The value of the root.

$\large\bf{\color{deepskyblue}{Solution}}$

 We have,

a = 1

b = -2

c = 9/4

$\large\bf{\color{green}{Formula~Required}}$

$\underline {\large{\boxed {\red{\sf{D= b^2 - 4ac}}}}}$

Substituting the values in first formula :

$\begin{gathered} \implies \sf{D= b^2 - 4ac} \\ \\\end{gathered}$

$\begin{gathered} \implies \sf{D= ( - 2)^2 - \cancel{4}\times 1\times \dfrac{9}{\cancel{4}} } \\ \\\end{gathered}$

$\begin{gathered} \implies \sf{D= 4 - 9} \\ \\\end{gathered}$

$\implies\underline{\underline{\large{\boxed{\pink{\bf{D= -5}}}}}}$

∴ Here , D < 0 so roots are not real and unequal.