If one root of the quadratic equation kx2 – 20x + 34 = 0 is 5 – 2√2 , find k.

7. If one root of the quadratic equation kx² – 20x + 34 = 0 is 5 – 2√2 , find k.

Sol. kx² – 20x + 34 = 0

Comparing with ax² + bx + c = 0 we have a = k, b = – 20, c = 34

Let  α  and β be the roots of given quadratic equation.

∴ α  = 5 – 2√2 [Given]

∴  β  = 5 + 2 √2

∴  α  + β  = – b/a = –(– 20)/k = 20/k

∴  5 – 2√2 + 5 + 2√2 = 20/k

∴  10 = 20/k

∴ k = 20/10

∴  k = 2