Question Bank - Mathematics

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If the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?

A.
a + b + c = 0
B.
a - b + c = 0
C.
a + b - c = 0
D.
-a + b + c = 0

Solution:

Concept:For a quadretic equation ax2 + bx + c = 0,Discriminent (D) = b2 - 4acFor equal roots, D = 0Formula used:(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2caCalculation:Given that,x2 - ax - bx - cx + bc + ca = 0? x2 - (a + b + c)x + bc + ca = 0For equal root, D = 0? [-(a + b + c)]2 - 4(bc + ca) = 0? a2 + b2 + c2 + 2ab + 2bc + 2ca - 4bc - 4ca = 0? a2 + b2 + c2 + 2ab - 2bc - 2ca = 0Using the above formula, we can write(a + b - c)2 = 0? a + b - c = 0

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