Question

The value of p for which the roots of the equation px(x – 2) + 6 = 0 are equai is -------- ​

Answer 1

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Step-by-step explanation:

The given quadratic equation is px(x − 2) + 6 = 0. Let us factorize the given quadratic equation. Since the roots of the given quadratic equation are equal, its discriminant is equal to 0. Thus, the value of p is 0 or 6.

Answer 2

Answer:

6

Step-by-step explanation:

Given quadratic equation is px (x – 2) + 6 = 0 ⇒ px2 − 2px + 6 = 0 … (1) By comparing equation (1)with ax2 + bx + c = 0, we get a = p, b = −2p and c = 6. Since given that the given quadratic equation has equal roots. ∴ D = b2– 4ac = 0 (∵ for equal roots D = 0) ⇒(−2p)2 − 4 × p × 6 = 0 ⇒ 4p2 − 24p = 0 ⇒ 4p (p – 6) = 0 ⇒ p = 0 or p – 6 = 0 ⇒ p = 0 or p = 6 but p ≠ 0 (∵ If p = 0 then given equation is not quadratic equation)

Hence the value of p is 6, for which the given quadratic equation have equal roots.