If $x^2 - 6x + 5 = 0$ and $x^2 - 3ax + 35 = 0$ have a common root, then find $a$.

If x² - 6x + 5 = 0 and x² - 3ax + 35 = 0 have a co – Class 12 Mathematics

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x^2 - 6x + 5 = 0

Telangana TsbieTelangana Board of Intermediate Education 2024Subjective· 2mImportance★★★★★

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Factor the first quadratic to get its roots, then substitute each root into the second equation to find $a$ .

$x^2-6x+5=0 \Rightarrow (x-1)(x-5)=0 \Rightarrow x=1 \text{ or } x=5$ .

The common root must be either $1$ or $5$ , and it must also satisfy $x^2-3ax+35=0$ .

Case 1: common root $=1$ …