Chapter P.5, Problem 3E

Solution

To solve the equation graphically by finding x-intercepts. Confirm by using factoring the equation, $4x^2-8x+3=0$ .

  $x=\{0\cdot 5,1\cdot 5\}$

Given:

The equation is, $4x^2-8x+3=0$

Concept Used:

• The x-intercept is given by y = 0: 0 = ax² + bx + c. Isolating the square and then applying the square root property.
• The discriminant gives the number of x-intercepts of a quadratic function, because it gives us the number of solutions to ax² + bx + c = 0.

Calculation:

  $4x^2-8x+3=0$

Let y=0

So $4x^2-8x+3=y$

The graph of $4x^2-8x+3=y$

is shown below:

  

Since the graph intersects the x- axis at $x=0\cdot 5$ and $x=1\cdot 5$ , so the solutions are $x=\{0\cdot 5,1\cdot 5\}$

Now solve by factoring method-

  $\begin{array}{c}4x^2-8x+3=0\\ 4x^2-(6+2)x+3=0\\ 4x^2-6x-2x+3=0\\ 2x(2x-3)-1(2x-3)=0\\ (2x-1)(2x-3)=0\\ (2x-1)=0\\ 2x=1\\ x=\frac{1}{2}\\ x=0\cdot 5\\ (2x-3)=0\\ 2x=3\\ x=\frac{3}{2}\\ x=1\cdot 5\\ x=\{0\cdot 5,1\cdot 5\}\end{array}$

Both from graphically and factoring solution is same i.e $x=\{0\cdot 5,1\cdot 5\}$

Thus, the solution of the given equation is $x=\{0\cdot 5,1\cdot 5\}$ .