यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को (-1) पर काटता है और (2) पर छूता है तो अलग-अलग वास्तविक शून्यक कितने हैं?
If the graph of a cubic polynomial crosses the (x)-axis at (-1) and touches it at (2), how many distinct real zeroes are there?
#cubic
#distinct-zeroes
#graph
A दो / Two
B तीन / Three
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 3
Exam Tip
अलग-अलग शून्यक केवल (-1) और (2) हैं। छूने वाला शून्यक दोहराया हो सकता है पर अलग मान एक ही गिना जाता है।
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यदि (p(x)=x-3 -25x) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=x-3 -25x), at how many distinct points will the graph cut the (x)-axis?
#cubic
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
(x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 3
Exam Tip
(x-3 -25x=x(x-5)(x+5)) है इसलिए तीन अलग शून्यक हैं। टिप: पहले सामान्य गुणनखंड निकालें।
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यदि (p(x)=x-3 -16x) है, तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=x-3 -16x), at how many distinct points will the graph cut the (x)-axis?
#cubic
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
(x-3 -16x=x(x-4)(x+4)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -16x=x(x-4)(x+4)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 3
Exam Tip
(x-3 -16x=x(x-4)(x+4)) है, इसलिए तीन अलग शून्यक हैं। टिप: पहले सामान्य गुणनखंड निकालें।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर छूता और काटता है, तो अलग वास्तविक शून्यक कितने होंगे?
If the graph of a cubic polynomial touches or crosses the (x)-axis at two distinct points, how many distinct real zeroes will it have?
#cubic
#distinct zeroes
#graph reading
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 3
Exam Tip
अलग शून्यक अलग (x)-अक्ष मिलने वाले बिंदुओं की संख्या से मिलते हैं। टिप: घात से अधिकतम संख्या मिलती है, वास्तविक गिनती ग्राफ से पढ़ें।
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यदि (p(x)=x-3 -9x) है, तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काट सकता है?
If (p(x)=x-3 -9x), at how many distinct points can the graph cut the (x)-axis?
#cubic
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
(x-3 -9x=x(x-3)(x+3)), so there are three distinct zeroes. Tip: take the common factor and use difference of squares.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -9x=x(x-3)(x+3)), so there are three distinct zeroes. Tip: take the common factor and use difference of squares.
Step 3
Exam Tip
(x-3 -9x=x(x-3)(x+3)), इसलिए तीन अलग शून्यक हैं। टिप: सामान्य गुणनखंड निकालकर वर्गों का अंतर देखें।
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