Question

If alpha and beta are the zeros of the quadratic polynomial x2-3x+q what is the value of q if 2 alpha =3 beta

Answer 1

Polynomials :

         ↓

• Sum of zeros = - Coefficient of x/Coefficient of x²

• Product of zeros = Constant Term/Coefficient of x²

Solution :

     ↓

$\bold{\Longrightarrow{p(x) = {x}^{2}- 3x + q}} \\ \\ \bold{\Longrightarrow{\alpha + \beta = -(- 3)}} \\ \bold{\Longrightarrow{\alpha+\beta = 3.....(1)}} \\ \\\bold{\Longrightarrow{2\alpha = 3 \beta}} \\\bold{\Longrightarrow{2\alpha - 3\beta= 0....(2)}} \\ \\ \bold{\Longrightarrow{On \: doing \: 3 \times (1)}} \\ \\ \bold{\Longrightarrow{3\alpha + 3\beta= 9.....(3)}} \\ \\ \bold{\Longrightarrow{On \: doing \: (2)+(3)}} \\ \\ \bold{\Longrightarrow{5\alpha = 9}}$

→ α = 9/5

Then, β = 3 - 9/5 = (15 - 9)/5

→ 6/5

∴ αβ = 9/5 × 6/5 = q

⇒ 54/25 = q

• Answer : 54/25