Question

При каком значении "а" один из корней уравнения 3х^2+4х+а=0 равен 2?

Answer 1

3х^2+4x+a=0

3*2^2+4*2+a=0

12+8+a=0

20+a=0

a=0-20

a=-20

Answer 2

При значении "а" равном 8, один из корней уравнения 3х^2 + 4х + а = 0 будет равен 2.

Explanation:

To find the value of "a" for which one of the roots of the equation 3х^2 + 4х + а = 0 is equal to 2, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, we have a = 3, b = 4, and c = а. We want one of the roots to be equal to 2, so we can substitute x = 2 into the quadratic formula and solve for "a":

2 = (-4 ± √(4^2 - 4 * 3 * a)) / (2 * 3)

Simplifying this equation, we get:

2 = (-4 ± √(16 - 12a)) / 6

Multiplying both sides of the equation by 6, we get:

12 = -4 ± √(16 - 12a)

Squaring both sides of the equation, we get:

144 = 16 - 12a

Rearranging the equation, we get:

12a = 16 - 144

12a = -128

Dividing both sides of the equation by 12, we get:

a = -128 / 12

Simplifying this fraction, we get:

a = -32/3

Therefore, when "a" is equal to -32/3, one of the roots of the equation 3х^2 + 4х + а = 0 is equal to 2.