HELP PLS! THANK YOU SO MUCH! Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quadratic equation tell about the solutions to 3x^2-6=2x

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac informs us about the nature of the roots.

• If b² - 4ac > 0 then 2 real and distinct roots ( solutions )

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then roots are not real

Given

3x² - 6 = 2x ( subtract 2x from both sides )

3x² - 2x - 6 = 0 ← in standard form

with a = 3, b = - 2, c = - 6 , thus

b² - 4ac = (- 2)² - ( 4 × 3 × - 6) = 4 - (- 72) = 4 + 72 = 76

Since b² - 4ac > 0 then the solution is 2 real and distinct roots

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .