Question

If one root of the quadratic equation 3x^2+px+4=0 is 2/3, then find the value of p and the other root of the equation.​

Answer 1

EXPLANATION.

One roots of the quadratic equation,

⇒ F(x) = 3x² + px + 4 = 0. is 2/3.

As we know that,

put the value of x = 2/3 in equation, we get.

⇒ 3(2/3)² + p(2/3) + 4 = 0.

⇒ 3(4/9) + 2p/3 + 4 = 0.

⇒ 4/3 + 2p/3 + 4 = 0.

⇒ 4 + 2p + 12 = 0.

⇒ 2p + 16 = 0.

⇒ 2p = -16.

⇒ p = -8.

                                                                                                                   

MORE INFORMATION.

Quadratic expression.

A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called a quadratic expression in x.

The quadratic equation.

ax² + bx + c = 0 ( a ≠ 0 ) has two roots, given by.

α = -b + √D/2a.

β = -b - √D/2a.

D= Discriminant.

D = b² - 4ac.

Answer 2

Step-by-step explanation:

Question:

If one root of the quadratic equation 3x^2+px+4=0 is 2/3, then find the value of p and the other root of the equation.

Given:

• 2/3 is one of the root of the quadratic equation: 3x^2+px+4=0

To find:

• p
• Other root of the equation

Solution:

As 2/3 is one root of the equation, let us apply it in the x:

3x^2+px+4=0

3(2/3)^2+(2/3)p+4=0

3(4/9)+(2/3)p+4=0

4/3+2p/3+4=0

16/3+2p/3=0

2p/3= -16/3

p= -16/3 $\times$ 3/2

p = -8

3x^2+px+4=0

Substitute p = -8

3x^2 - 8x + 4 = 0

3x^2 - 6x - 2x + 4 = 0

3x(x-2) -2(x-2)

(3x-2)=0 and x-2=0

3x = 2 and x = 2

x = 2/3 or x = 2

Hence, the other root of the quadratic equation is: x = 2