Question

Determine and describe the ​number​ and ​type​ of roots of the quadratic functions. Show any and all work necessary to determine your answer. Justify your answer with appropriate reasoning. a) y=3x^2+7x+8 b) y=2x^2-7x-2 c) y=9x^2+30+25

Answer 1

See explanations below

Explanation:

The root of a quadratic equation is determined by its discriminant

D = b²-4ac

If D > 0, the roots are real and unique

If D < 0, the roots are complex

If D= 0, the roots are real and equal

a) For the quadratic equation

y=3x^2+7x+8

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 3, b = 7 and c = 8

Get the discriminant

D = 7²-4(3)(8)

D = 49 - 96

D = -47

Since the discriminant value is less than 0, hence the roots are complex roots

b) For the quadratic equation

y=2x^2-7x-2

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 2, b = -3 and c = -2

Get the discriminant

D = (-3)²-4(2)(-2)

D = 9 + 16

D = 25

Since the discriminant value is greater than 0, hence the roots are real and unique.

c) For the quadratic equation

y=9x^2+30x+25

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 9, b = 30 and c = 25

Get the discriminant

D = 30²-4(9)(25)

D = 900 - 900

D = 0

Since the discriminant value is equal to 0, hence the roots are complex real and equal