6th q

6th q solutim of 6 • X — O. For value Of k. (4 — + (2k •u • is Solve by factorization — — 21 O. If one rcH)t is equal to the square Of the other the • - O. value of k? — : If the roots Of the equation (x — a) (x — b) — k O are c and d, men move (x—c) are a and b-

Hi! Here is the answer to your question. The given quadratic equation is (x – a) (x – b) + (x – b) (x – c) + (x – a) (x – c) = 0 ⇒ x2 – ax – bx + ab + x2 – bx – cx + bc + x2 – cx – ax + ca = 0 ⇒ 3x2 – 2(a + b + c) x + (ab + bc + ca) = 0 Discriminant, D = [–2 (a + b + c)]2 – 4 × 3 × (ab + bc + ca) = 4 (a+ b + c)2 – 12 (ab + bc + ca) = 4 (a2+ b2 + c2 + 2ab + 2bc + 2ca – 3ab – 3bc – 3ca) ∴ D > 0. So, the roots the given quadratic equation are real. When a = b = c, D = 2 × 0 = 0. Thus, the roots of the given quadratic equation are equal. Cheers!