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

Question

Question

Answer 1

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

⇒ - 15 α = -β/4

⇒ 15 α = β/4

⇒ 15 = β/4 (∵ α = 1)

∴ β = 60

Hence, option (2) is correct.

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