If $x^{2} - 6 x + 5 = 0$ and $x^{2} - 12 x + p = 0$ have a common root, then find p.

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Solution

$x^{2} - 6 x + 5 = 0 ⟹ x^{2} - 5 x - x + 5 = 0 ⟹ x (x - 5) - (x - 5) = 0 ⟹ (x - 1) (x - 5) = 0 ⟹ x = 1, 5$
If $x = 1$ be the common root then $(1)^{2} - 12 (1) + p = 0 ⟹ p = 11$
If $x = 5$ be the common root then $(5)^{2} - 12 (5) + p = 0 ⟹ p = 35$

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If x2−6x+5=0 and x2−12x+p=0 have a common root, then find p.

x2−6x+5=0⟹x2−5x−x+5=0⟹x(x−5)−(x−5)=0⟹(x−1)(x−5)=0⟹x=1,5If x=1 be the common root then (1)2−12(1)+p=0⟹p=11If x=5 be the common root then (5)2−12(5)+p=0⟹p=35

If $x^{2} - 6 x + 5 = 0$ and $x^{2} - 12 x + p = 0$ have a common root, then find p.

$x^{2} - 6 x + 5 = 0 ⟹ x^{2} - 5 x - x + 5 = 0 ⟹ x (x - 5) - (x - 5) = 0 ⟹ (x - 1) (x - 5) = 0 ⟹ x = 1, 5$
If $x = 1$ be the common root then $(1)^{2} - 12 (1) + p = 0 ⟹ p = 11$
If $x = 5$ be the common root then $(5)^{2} - 12 (5) + p = 0 ⟹ p = 35$