Question 1/4
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p(x)=x-2 -\sqrt{5}x), तो इसके शून्यक कौन से हैं?
If (p(x)=x-2 -\sqrt{5}x), what are its zeroes?
#factorisation
#zeroes
#irrational
A \(0,\sqrt{5}\)
B \(1,\sqrt{5}\)
C \(0,-\sqrt{5}\)
D \(\sqrt{5},-\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(0,\sqrt{5}\)
Step 1
Concept
(p(x)=x\(x-\sqrt{5}\)), so the zeroes are (0) and \(\sqrt{5}\). Taking the common factor is a fast method in exams.
Step 2
Why this answer is correct
The correct answer is A. \(0,\sqrt{5}\). (p(x)=x\(x-\sqrt{5}\)), so the zeroes are (0) and \(\sqrt{5}\). Taking the common factor is a fast method in exams.
Step 3
Exam Tip
(p(x)=x\(x-\sqrt{5}\)), इसलिए शून्यक (0) और \(\sqrt{5}\) हैं। परीक्षा में सामान्य गुणनखंड निकालना तेज तरीका है।
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Question 2/4
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p(x)=x-2 -2\sqrt{2}x+2) है, तो (p(x)) का सही गुणनखंड रूप कौन सा है?
If (p(x)=x-2 -2\sqrt{2}x+2), which is the correct factorized form of (p(x))?
#factorisation
#perfect-square
#irrational
A (\(x-\sqrt{2}\)2 )
B (\(x+\sqrt{2}\)2 )
C ((x-2)2 )
D (\(x-\sqrt{2}\)\(x+\sqrt{2}\))
Explanation opens after your attempt
Correct Answer
A. (\(x-\sqrt{2}\)2 )
Step 1
Concept
(x-2 -2\sqrt{2}x+2=\(x-\sqrt{2}\)2 ). Recognizing a perfect square gives equal irrational zeroes.
Step 2
Why this answer is correct
The correct answer is A. (\(x-\sqrt{2}\)2 ). (x-2 -2\sqrt{2}x+2=\(x-\sqrt{2}\)2 ). Recognizing a perfect square gives equal irrational zeroes.
Step 3
Exam Tip
(x-2 -2\sqrt{2}x+2=\(x-\sqrt{2}\)2 ) है। पूर्ण वर्ग पहचानने से समान अपरिमेय शून्यक मिलते हैं।
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Question 3/4
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -11x+30) का ग्राफ खींचा जाए तो (x)-अक्ष पर कौन से बिंदु मिलेंगे?
If the graph of (p(x)=x-2 -11x+30) is drawn, which points will lie on the (x)-axis?
#quadratic
#factorisation
#graph-points
A ((5,0)) और ((6,0)) / ((5,0)) and ((6,0))
B ((-5,0)) और ((-6,0)) / ((-5,0)) and ((-6,0))
C ((0,5)) और ((0,6)) / ((0,5)) and ((0,6))
D ((30,0)) और ((11,0)) / ((30,0)) and ((11,0))
Explanation opens after your attempt
Correct Answer
A. ((5,0)) और ((6,0)) / ((5,0)) and ((6,0))
Step 1
Concept
(x-2 -11x+30=(x-5)(x-6)). So the graph meets the (x)-axis at (x=5) and (x=6).
Step 2
Why this answer is correct
The correct answer is A. ((5,0)) और ((6,0)) / ((5,0)) and ((6,0)). (x-2 -11x+30=(x-5)(x-6)). So the graph meets the (x)-axis at (x=5) and (x=6).
Step 3
Exam Tip
(x-2 -11x+30=(x-5)(x-6)) है। इसलिए (x=5) और (x=6) पर ग्राफ (x)-अक्ष से मिलता है।
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Question 4/4
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
द्विघात (p(x)=x-2 +2x-15) का ग्राफ (x)-अक्ष को किन (x)-मानों पर काटेगा?
At which (x)-values will the graph of (p(x)=x-2 +2x-15) cut the (x)-axis?
#quadratic
#factorisation
#x-intercepts
A (3) और (-5) / (3) and (-5)
B (-3) और (5) / (-3) and (5)
C (5) और (3) / (5) and (3)
D (-5) और (-3) / (-5) and (-3)
Explanation opens after your attempt
Correct Answer
A. (3) और (-5) / (3) and (-5)
Step 1
Concept
(x-2 +2x-15=(x+5)(x-3)). Zeroes are the (x)-values of (x)-axis intersections.
Step 2
Why this answer is correct
The correct answer is A. (3) और (-5) / (3) and (-5). (x-2 +2x-15=(x+5)(x-3)). Zeroes are the (x)-values of (x)-axis intersections.
Step 3
Exam Tip
(x-2 +2x-15=(x+5)(x-3)) है। शून्यक (x)-अक्ष पर कटान के (x)-मान होते हैं।
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