The quadratic expression is written as

MATHEMATICS · Single correct · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

The quadratic expression 2x2−8x+32x^{2}-8x+3 is written as 2(x−α)(x−β)2(x-\alpha)(x-\beta), where α\alpha and β\beta are real numbers. Which ordered pair (α,β)(\alpha,\beta) is correct? (a) (2+10, 2−10)\left(2+\sqrt{10},\,2-\sqrt{10}\right) (b) (−2+102, −2−102)\left(-2+\dfrac{\sqrt{10}}{2},\,-2-\dfrac{\sqrt{10}}{2}\right) (c) (2+102, 2−102)\left(2+\dfrac{\sqrt{10}}{2},\,2-\dfrac{\sqrt{10}}{2}\right) (d) (2+52, 2−52)\left(2+\dfrac{\sqrt{5}}{2},\,2-\dfrac{\sqrt{5}}{2}\right)

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