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प्रश्न
Find the value of p for which the roots of the equation px (x − 2) + 6 = 0, are equal.
उत्तर
The given quadratic equation is px(x − 2) + 6 = 0.
Let us factorize the given quadratic equation.
px(x − 2) + 6 = 0
∴ px2 − 2px + 6 = 0
Since the roots of the given quadratic equation are equal, its discriminant is equal to 0.
⇒ D = 0
⇒ b2 − 4ac = 0
⇒ (− 2p)2 − 4 × p × 6 = 0 [a = p, b = −2p, c = 6]
⇒ 4p2 − 24p = 0
⇒ 4p (p − 6) = 0
⇒ 4p = 0 or p − 6 = 0
⇒ p = 0 or p = 6
Thus, the value of p is 0 or 6.
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