Question

The ratio of the sum of the roots and their product of the quadratic
Equation 3x2 – 2x + 1 = 0 is .........​

Answer 1

Answer :

• Ratio = 2 : 1

S O L U T I O N :

Given,

• Quadratic equation, 3x² - 2x + 1 = 0.

To Find,

• The ratio of the sum of roots and product of roots.

Explanation,

Given, Quadratic equation, 3x² - 2x + 1 = 0.

On comparing with, ax² + bx + c = 0, We get;

⇒ a = 3 , b = -2 , c = 1

Sum of roots,

⇒ α + β = -b/a

⇒ α + β = -(-2)/3

⇒ α + β = 2/3

Product of roots,

⇒ αβ = c/a

⇒ αβ = 1/3

Now,

Ratio = Sum of roots / Product of roots

⇒ Ratio = 2/3 / 1/3

⇒ Ratio = 2/3 × 3/1

⇒ Ratio = 2/1

⇒ Ratio = 2 : 1

Therefore,

The ratio of sum and roots and product of roots is 2 : 1.