The two roots of a quadratic equation are α and β such that α + β = 10 and α - β = 4. The equation can be written as:

- x
^{2}– 10x + 21 = 0 - x
^{2}– 12x + 21 = 0 - x
^{2}– 8x + 21 = 0 - x
^{2}– 10x + 24 = 0 - None of these

Option 1 : x^{2} – 10x + 21 = 0

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RBI Grade B 2020: Full Mock Test

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**Given:**

Roots of equation: α and β

α + β = 10 and α - β = 4

**Concept Used:**

x^{2} - ( sum of the roots) x + product of the roots = 0

**Calculation:**

α + β = 10 and α - β = 4

2α = 14

⇒ α = 7 and β = 3

Sum of roots = (α + β) = 10

Products of roots = αβ = (7)(3) = 21

The required equation is –

⇒ x^{2} – (α + β)x + (αβ) = 0

⇒ x^{2} – 10x + 21 = 0

**∴ The equation can be written as x2 – 10x + 21 = 0.**

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