Chapter 9.6, Problem 61PFA

(a)

To determine

Solve the equation.

Answer to Problem 61PFA

Option A

Explanation of Solution

Given Information: $3x^2-4x+2=0$

Formula Used: $D=b^2-4ac$

Calculation:

• $D$ equal to negative so $x$ has no real solution.
• $D$ equal to 0 so $x$ has 1 real solution.
• $D$ equal to positive so $x$ has 2 real solution.

  $3x^2-4x+2=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=3,b=-4$ and $c=2$

  $D={\left(-4\right)}^2-4\times 3\times 2$

Now,

  $D=16-24$

Hence,

  $D=-8$

Option A. It is a negative integer

(b)

To determine

Solve the equation.

Answer to Problem 61PFA

Option D

Explanation of Solution

Given Information: $3x^2-4x+2=0$

Formula Used: $D=b^2-4ac$

Calculation:

• $D$ equal to negative so $x$ has no real solution.
• $D$ equal to 0 so $x$ has 1 real solution.
• $D$ equal to positive so $x$ has 2 real solution.

  $3x^2-4x+2=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=3,b=-4$ and $c=2$

  $D={\left(-4\right)}^2-4\times 3\times 2$

Now,

  $D=16-24$

Hence,

  $D=-8$

Option D. As, $D$ equal to negative so $x$ has no real solution