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in Quadratic Equations by (237k points)
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5x2 - 8x – α = 0 has roots -5 and 2β .What is the value of α
1. 11
2. 165
3. 33
4. 33/10

1 Answer

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Best answer
Correct Answer - Option 2 : 165

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 is 5x2 - 8x – α = 0 and roots are -5 and 2β

Now, sum of roots = -5 + 2β = -(-8)/5 = 8/5

⇒ 2β = 8/5 + 5  = 33/5

Now, Product of the roots = (-5)(2β) = -α/5

⇒ -5(33/5) = -α/5

⇒ α = 33 × 5 = 165

Hence, option (2) is correct. 

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