i need help -5v^2=2v

Question

find the discriminant of each quadratic equation then state the number and type of solutions. another problem is 10x^2-6=7x

Answer 1

Given a quadratic of form ax² + bx + c = 0

x = [-b ±√(b²-4ac)]/2

 

Discriminant is the part under the radical: b² - 4ac  

1)  If the discriminant is equal to zero there is one real root which is a double root

2)  If the discriminant is greater than zero there are two real roots.

     If it is a perfect square the real roots are rational.  If not, they are irrational.

3)  If the discriminant is less than zero there are two complex roots that are 

     complex conjugates of each other.

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-5v² = 2v

5v² + 2v = 0

For quadratic equation purposes:  a=5, b=2, c=0

 

b² - 4ac = 2² - 4(5)(0) = 4

Since 4>0 there are two rational real roots since 4 is a perfect square of 2

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10x² - 6 = 7x

10x² - 7x - 6 = 0

a=10, b=-7, c=-6

 

b² - 4ac = (-7)² -4(10)(-6)

= 49 + 240

= 289

= 17²

 

Since the discriminant is greater than zero and a perfect square,

again we have two rational real roots.