Question

the equation whose roots are double the roots of equation x² + 6x + 3 = 0 is _​

Answer 1

Answer:-

Given quadratic equation is x² + 6x + 3 = 0.

Let the roots of the equation be α & β.

On comparing it with the standard form of a quadratic equation i.e., ax² + bx + c = 0 ;

Let,

• a = 1
• b = 6
• c = 3.

We know that,

Sum of the roots = - b/a

⟹ α + β = - 6/1

⟹ α + β = - 6 -- equation (1)

Product of the roots = c/a

⟹ αβ = 3/1

⟹ αβ = 3 -- equation (2).

Now,

We have to find the quadratic equation whose roots are double the roots of the given quadratic equation. (whose roots are 2α & 2β).

We know,

General form of a quadratic equation is x² - (sum of the roots)x + Product of the roots = 0.

Hence,

Required quadratic equation:

⟹ x² - (2α + 2β)x + (2α)(2β) = 0

⟹ x² - 2(α + β)x + 4αβ = 0

Putting the respective values from equations (1) & (2) we get,

⟹ x² - 2x( - 6) + 4(3) = 0

⟹ x² + 12x + 12 = 0

∴ Required quadratic equation is x² + 12x + 12 = 0 (Option - C).