Question

5.Find the roots of the parabola given by the following equation.

Answer 1

Answer:

Part 5) The roots are x=-3 and x=1.5

Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)

Step-by-step explanation:

Part 5) Find the roots of the parabola given by the following equation

$2x^{2} +5x-9=2x$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$2x^{2}+5x-2x-9=0$

$2x^{2}+3x-9=0$

so

$a=2\\b=3\\c=-9$

substitute in the formula

$x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}$

$x=\frac{-3(+/-)\sqrt{81}} {4}$

$x=\frac{-3(+/-)9} {4}$

$x=\frac{-3(+)9} {4}=1.5$

$x=\frac{-3(-)9} {4}=-3$

therefore

The roots are x=-3 and x=1.5

Part 6) Solve the inequality and graph the solution on a number line.

$-3(5y-4)\geq 17$

Solve for y

$-15y+12\geq 17$

Subtract 12 both sides

$-15y\geq 17-12$

$-15y\geq 5$

Multiply by -1 both sides

$15y\leq -5$

Divide by 15 both sides

$y\leq -1/3$

The solution is the interval -----> (-∞, -1/3]

All  real numbers less than or equal to negative one third

The solution on a number line is the shading area below of the line y=-1/3 (close circle)

The graph in the attached figure