If α, β are the zeros of the polynomial (x 2 - x - 12), then form a quadratic equation whose zeros are 2α and 2β.

Question

Philoid · Accepted Answer

Given Equation : x² - x - 12 = 0

which is of the form ax² + bx + c = 0 (General Form)

The product of the roots of the general form of equation

Sum of Roots of the general equation =

So

⇒ α + β = 1

⇒ 2(α + β) = 2 ….Equation 1

Similarly

α×β = -12

⇒ 2α×2β = -48 …Equation 2

The new equation will be formed by combining the results of Equation 1 & 2

The New Polynomial Formed from the new roots is x² -2x-48