If x2−ax−21=0 and x2−3ax+35=0;a>0 have a common root, then a is equal to:
A
1
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B
2
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C
4
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D
5
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Solution
The correct option is C 4 Let α be a common root of the two given equations, then α2−3aα+35=0 and α2−aα−21=0. On substracting we get −2aα+56=0orα=28a. As α is a root of x2−ax−21=0, ∴(28a)2−a(28a)−21=0 Or a2=42ora=±4 ∴a>0, we get a = 4