5. A rectangular picture is 4 cm longer than it is wide. It is surrounded by a mat that is 2 cm wide. The combined area of the picture and the mat is 140 cm2. Find the dimensions of the picture.
8. What is the smallest integer value of c for which the equation 2x^2 - 7x +c =0 has no real roots?
Solve and show work! Thanks!
8. What is the smallest integer value of c for which the equation 2x^2 - 7x +c =0 has no real roots?
Solve and show work! Thanks!
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8. What is the smallest integer value of c for which the equation 2x^2 - 7x +c =0 has no real roots?
take c=0 then:
y= 2x^2-7x = 2X^2 -7X+0
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, -6.125)
factors: (2X -7)(X+0)
if you move the parabola up 6 units the roots are:
y= 2x^2-7x+6 = 2X^2 -7X +6
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, -0.125)
positive discriminant = 1; two real roots: 1.5 and 2
if you go up 7 units then:
y= 2x^2-7x+7 = 2X^2 -7X +7
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, +0.875)
negative discriminant = -7; two complex roots: 1.75±0.6614i
take c=0 then:
y= 2x^2-7x = 2X^2 -7X+0
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, -6.125)
factors: (2X -7)(X+0)
if you move the parabola up 6 units the roots are:
y= 2x^2-7x+6 = 2X^2 -7X +6
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, -0.125)
positive discriminant = 1; two real roots: 1.5 and 2
if you go up 7 units then:
y= 2x^2-7x+7 = 2X^2 -7X +7
Axis of symmetry: X=1.75; Vertex (minimum): (1.75, +0.875)
negative discriminant = -7; two complex roots: 1.75±0.6614i