Question

3x² – 8x – 3 = 0, x = 9, $\frac{1}{2}$, 3

Answer 1

Given: 3x² – 8x – 3 = 0 and x = 9, $\frac{1}{2}$ and 3.
we have to determine if the given values of x satisfy the quadratic equation
On substituting x = 9 in L.H.S. of the given equation, we get:
3(9)² – 8(9) – 3
= 243 – 72 – 3
= 168
=> L.H.S. $\ne$ R.H.S.
Thus, x = 9 does not satisfy the given equation.
Therefore, x = 9 is not a root of the given quadratic equation.

On substituting x =$\frac{1}{2}$ in L.H.S. of the given equation, we get:

$$\begin{gathered} 3{\left(\frac{1}{2}\right)}^2-8\left(\frac{1}{2}\right)-3 \\ =\frac{3}{4}-4-3 \\ =\frac{3}{4}-7 \\ =\frac{3-28}{4}=\frac{-25}{4} \end{gathered}$$

=> L.H.S. $\ne$ R.H.S.
Thus, x = $\frac{1}{2}$ does not satisfy the given equation.
Therefore, x =$\frac{1}{2}$ is not a root of the given quadratic equation.

On substituting x = 3 in L.H.S. of the given equation, we get:
3(3)² – 8(3) – 3
= 27 – 24 – 3
= 0
=> L.H.S. = R.H.S.
Thus, x = 3 satisfies the given equation.
Therefore, x = 3 is a root of the given quadratic equation.