Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 571-580 of 600 questions.
If (p(x)=4x-2-4x+1), what are its zeroes?
A. \(\frac{1}{2},\frac{1}{2}\)
(4x-2-4x+1=(2x-1)2), इसलिए शून्यक \(\frac{1}{2}\) दो बार है। पूर्ण वर्ग रूप तुरंत समान शून्यक देता है। / (4x-2-4x+1=(2x-1)2), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
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If (p(x)=x-4-5x-2+4), what are its real zeroes?
A. -(2,-1,1,2)
(x-4-5x-2+4=\(x^2-1\)\(x^2-4\)) है। इसलिए वास्तविक शून्यक (-2,-1,1,2) हैं। / (x-4-5x-2+4=\(x^2-1\)\(x^2-4\)). Therefore the real zeroes are (-2,-1,1,2).
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If the zeroes of (p(x)=x-3+ax-2+bx-12) are (1,3,-4), what is (a+b)?
A. -(9)
योग (1+3-4=0) है, इसलिए (a=0)। युग्म गुणनफलों का योग (3-4-12=-13), इसलिए (b=-13) और (a+b=-13)। / The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).
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If (p(x)=x-3-9x), how many distinct real zeroes does it have?
A. (3)
(x-3-9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं। / (x-3-9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
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If (p(x)=x-2-2x-8), what are the zeroes of (p(x+3))?
A. -(5,1)
(p(x)) के शून्यक (4) और (-2) हैं। (x+3=4) या (x+3=-2) से शून्यक (1) और (-5) मिलते हैं। / The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).
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If (p(x)=x-2-5x+6), what is the value of (p(2)+p(3))?
A. (0)
(2) और (3), (p(x)) के शून्यक हैं, इसलिए (p(2)=0) और (p(3)=0)। इसलिए योग (0) है। / (2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).
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If (p(x)=ax-2+bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?
A. (p(x)) शून्य बहुपद है(p(x)) is the zero polynomial
अधिकतम द्विघात बहुपद के तीन अलग-अलग शून्यक तभी हो सकते हैं जब वह शून्य बहुपद हो। घात से अधिक अलग शून्यक असंभव होते हैं। / A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.
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If the zeroes of (p(x)=x-2-kx+36) are positive and in the ratio (1:4), what is (k)?
A. (15)
शून्यक (t) और (4t) मानें, तो \(4t^2=36\) से (t=3) है। योग (15) है, इसलिए (k=15)। / Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).
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If (p(x)=2x-2-7x+5), what is the difference between the sum and product of its zeroes?
A. (1)
योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है। / The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
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If the value of (p(x)=x-3+mx-10) at (x=2) is (0), what is (m)?
A. (1)
(p(2)=8+2m-10=0) है। इससे (2m=2) और (m=1) मिलता है। / (p(2)=8+2m-10=0). This gives (2m=2) and (m=1).
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