Use the discriminant to describe the roots of each equation. Then select the best description.

1. x^2 - 5x + 7 = 0
2. x^2 - 5x - 4 = 0
3. 16x^2 + 8x + 1 = 0
4. x^2 + 9x + 14 = 0

Question

Use the discriminant to describe the roots of each equation. Then select the best description.

1. x^2 - 5x + 7 = 0
2. x^2 - 5x - 4 = 0
3. 16x^2 + 8x + 1 = 0
4. x^2 + 9x + 14 = 0

anonymous · Answer

here are the options 

a.double root
b.real and rational root
c.real and irrational root
d.imaginary root

campbell_st · Answer

do you know how to use the discriminant..?

anonymous · Answer

no not really

anonymous · Answer

The discriminant is $$b^2 - 4ac$$

if the discriminant is positive, there are 2 real roots
if it is negative, then there are 2 imaginary roots
if it is 0, then there is one real root

shadowlegendx · Answer

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campbell_st · Answer

ok... so for a quadratic

$$ax^2 + bx + c$$

the discriminant is 

$$\Delta = b^2 - 4ac$$

in your 1st question a = 1, b = -5 and c = 7

can you substitute the values and calculate the value of the discriminant..?

campbell_st · Answer

the value will determine the type of roots your quadratic equation has

$$\Delta > 0$$

is 2 two unequal real roots

if the descriminant is a perfect square such as 1, 4, 9, 16, ... the the roots are rational... otherwise there are irrational. 

$$\Delta = 0$$

the two roots are equal.... e.f x^2 - 4x + 4 = (x-2)^2 and has 2 equal roots of x = 2

$$\Delta < 0$$

the roots are unreal... or complex... 

hope it helps

anonymous · Answer

ok so can you show me how you would solve #1

shadowlegendx · Answer

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anonymous · Answer

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anonymous · Answer

@ShadowLegendX

shadowlegendx · Answer

Lolz I do? :P

campbell_st · Answer

ok... in 1... 

a = 1 b = -5 and c = 7

using 

$$\Delta = b^2 - 4ac$$

so 

$$\Delta = (-5)^2 - 4 \times 1 \times 7$$

$$\Delta = 25 - 28$$

so 

$$\Delta= -3$$

this is less than zero... so it has complex or imaginary roots... 

hope it helps

anonymous · Answer

what about #2?

campbell_st · Answer

well a = 1, b = -5 and c = -4

so you can substitute them and see what you get...

anonymous · Answer

okay so i think its a.double root

campbell_st · Answer

well its 2 unequal roots that are irrational... this is because the answer is 39...

anonymous · Answer

what would this one be? 

x^2 - 6x + 12 = 0