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Question

Use the discriminant of te quadratic formula to determine the number of the roots for the 3x^2 - 7x + 4= 0. Then answer

•• How you would use the graph of this function to verify your answer?

Answer 1

The equation 3x² - 7x + 4 = 0

Compare it to quadratic equation ax² + bx + c = 0

a = 3, b = - 7, c = 4

Discriminant b² - 4ac = (- 7)² - 4(3)(4)

= 49 - 48

b² - 4ac = 1

Discriminant is positive, so we have two solutions.

Roots are x = [- b ± √(b² - 4ac)]/2a

x = [- (- 7) ± √1]/2(3)

x = ( 7 ± 1)/6

x = ( 7 + 1)/6 and x = (7 - 1)/6

x = 8/6 and x = 6/6

Roots are x = 4/3 and x = 1.

Check

Quadratic equation represents parabola.

Solutions of the quadratic function are x intercepts of parabola.

Choose random values for x and find the corresponding values for y.

x	y  = 3x2 - 7x + 4	(x, y)
0	y  = 3(0)2 -7(0) + 4	(0, 4)
0.5	y= 3(0.5)2-7(0.5)+4	(2, -3)
1.5	y= 3(1.5)2-7(1.5)+4	(1, 0)
2	y = 3(2)2 - 7(2) + 4	(2, 2)

Graph

Draw the coordinate plane.

Plot the points found in the table.

Connect the plotted points with smooth curve.

Observe the graph the x intercepts are 1 and 4/3.