Chapter 11.6, Problem 30PPSE

Solution

To identify:The correct option to solve $2x^2-7x-5$ .round answer to the nearest hundredth. $2x^2-7x-5$ .

Options (A) $-1.56,-4.44$

Options (B) $-5.44,1.56$

Options (C) $-0.61,4.11$

Options (D) $-5.56,-1.44$

Option (c) is correct option the required point is $\left(-0.61,4.11\right)$

Given information:

The given equation $2x^2-7x-5$ .

Explanation:

Consider the given information.

Put the value of option (b) into $2x^2-7x-5$

  $\begin{array}{c}x=-5.44\\ 2x^2-7x-5=2{\left(-5.44\right)}^2-7\left(-5.44\right)-5\\ =59.1872+38.08-5\\ =92.2672\\ x=1.56\\ 2x^2-7x-5=2{\left(1.56\right)}^2-7\left(1.56\right)-5\\ =4.8672-10.92-5\\ =-11.0528\end{array}$

These point does not satisfies the equation.

Put the value of option (b) into $2x^2-7x-5$

  $\begin{array}{c}x=-5.44\\ 2x^2-7x-5=2{\left(-5.44\right)}^2-7\left(-5.44\right)-5\\ =59.1872+38.08-5\\ =92.2672\\ x=1.56\\ 2x^2-7x-5=2{\left(1.56\right)}^2-7\left(1.56\right)-5\\ =4.8672-10.92-5\\ =-11.0528\end{array}$

This point does not satisfy the equation.

Put the value of option (c) into $2x^2-7x-5$

  $\begin{array}{c}x=-0.61\\ 2x^2-7x-5=2{\left(-0.61\right)}^2-7\left(-0.61\right)-5\\ =0.7442+4.27-5\\ =0.0142\\ x=4.11\\ 2x^2-7x-5=2{\left(4.11\right)}^2-7\left(4.11\right)-5\\ =33.7842-28.77-5\\ =0.0142\end{array}$

These points satisfy the equation to nearest hundredth.

Put the value of option (d) into $2x^2-7x-5$

  $\begin{array}{c}x=-5.56\\ 2x^2-7x-5=2{\left(-5.56\right)}^2-7\left(-5.56\right)-5\\ =61.8272+\mathrm{38.92.}-5\\ =95.7472\\ x=-1.44\\ 2x^2-7x-5=2{\left(-1.44\right)}^2-7\left(-1.44\right)-5\\ =4.1472+10.08-5\\ =9.2272\end{array}$

This point does not satisfy the equation.

So the correct option is (c).