Answer:
See explanations below
Step-by-step 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
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