If the roots of the quadratic equation px(x − 2) + 6 = 0 are equal,

1.	If the roots of the quadratic equation px(x − 2) + 6 = 0 are equal, find the value of p
Answer» 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.

If the roots of the quadratic equation px(x − 2) + 6 = 0 are equal, find the value of p

Answer»

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.

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