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If \(p(x)=x^3-3x^2-4x+12\), what is the product of \(p(2)\) and \(p(-2)\)?यदि \(p(x)=x^3-3x^2-4x+12\) है, तो \(p(2)\) और \(p(-2)\) का गुणनफल कितना होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 00
\(p(2)=2^3-3(2)^2-4(2)+12=8-12-8+12=0\), and \(p(-2)=(-2)^3-3(-2)^2-4(-2)+12=-8-12+8+12=0\). Therefore, \(p(2)\times p(-2)=0\times0=0\), so option B is correct. In an exam, remember that finding even one zero factor is sufficient to conclude that the entire product is zero.\(p(2)=2^3-3(2)^2-4(2)+12=8-12-8+12=0\) और \(p(-2)=(-2)^3-3(-2)^2-4(-2)+12=-8-12+8+12=0\)। अतः \(p(2)\times p(-2)=0\times0=0\), इसलिए सही उत्तर B है। परीक्षा में दोनों मान अलग-अलग निकालने के बजाय पहले यह जाँचें कि किसी एक मान का शून्य होना ही गुणनफल को शून्य बना देता है।
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