Question

find p, (p-12)x square -2(p-12)x +2=0 has equal roots

Answer 1

Answer:

p = 14

Assumption:

f(x) = (p - 12)x² - 2(p - 12)x + 2 = ax² + bx + c = 0

⇒ a = p - 12

⇒ b = -2(p - 12)

⇒ c = 2

Concept used:

If the roots of f(x) = ax² + bx + c = 0 are equal, then

c = b²/4a

[∵ As b² - 4ac = 0 here, b² = 4ac  →  b²/4a = c]

Step-by-step explanation:

⇒ According to c = b²/4a, it's  2 = (-2(p - 12))² / 4(p - 12)

$\Rightarrow\ c=\frac{b^2}{4a} \\ \\ \Rightarrow\ \frac{(-2(p-12))^2}{4(p-12)}=2 \\ \\ \Rightarrow\ \frac{4(p-12)^2}{4(p-12)}=2 \\ \\ \Rightarrow\ p-12=2 \\ \\ \Rightarrow\ p=\bold{14}$

⇒ Thus the answer is 14.