Question

If one of the root of quadratic equation X²- 10 X + 2 k =0 is( H + 2√6) then find the value of H and K

Answer 1

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Answer 2

Answer:

h+2 √6 is an irrational root.

Irrational roots always occur in conjugate pairs.

Therefore, h-2 √6 is also a root of the quadratic. Sum of the roots = - b/a

=> h+2 √6 + h-2 √6 = -(-10/1) = 10

=> 2h = 10 => h = 5.

Product of the roots = c/a

=> (h+2 √6)(h-2 √6) = 2k/1

=> (5+2 √6)(5–2√6) = 2k

=> 25- 24 = 2k => k = 1/2

Therefore, h = 5 and k = 1/2.

Step-by-step explanation: