Question

4x² + 8x – β = 0 has roots -5α and 3 .What is the value of β 

1. 1
2. 60
3. -60
4. 50

Answer 1

Correct Answer - Option 2 : 60

Concept:

Consider a quadratic equation: ax2 + bx + c = 0.

Let, α and β are the roots.

• Sum of roots = α + β = -b/a
• Product of the roots = α × β = c/a

 

Calculation:

Given quadratic equation: 4x2 + 8x – β = 0 and roots are -5α and 3

Now, sum of roots:

⇒ -5α + 3 = -(8)/4 = -2 

⇒ -5α = -5

⇒ α = 1

Now, Product of the roots:

⇒ (-5α)(3) = -β/4

⇒ 4 × (-5) × (3) = -β

⇒ β = 60

Hence, option (2) is correct.