Question 1/6
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि किसी द्विघात समीकरण की जड़ें (3) और (-2) हैं और \(x^2\) का गुणांक (2) है, तो समीकरण कौन-सा है?
If the roots of a quadratic equation are (3) and (-2), and the coefficient of \(x^2\) is (2), which is the equation?
#quadratic-roots
#forming-equation
#leading-coefficient
A \(2x^2-2x-12=0\)
B \(2x^2+2x-12=0\)
C \(2x^2-2x+12=0\)
D \(x^2-x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-2x-12=0\)
Step 1
Concept
The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-2x-12=0\). The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 3
Exam Tip
मॉनिक समीकरण \(x^2-x-6=0\) है। \(x^2\) का गुणांक (2) चाहिए, इसलिए पूरे समीकरण को (2) से गुणा करें।
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Question 2/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=4) समीकरण \(ax^2-10x+8=0\) का मूल है तो (a) का मान क्या है?
If (x=4) is a root of \(ax^2-10x+8=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) gives (16a-40+8=0), so (16a=32) and (a=2). Substitute when a coefficient is unknown.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=4) gives (16a-40+8=0), so (16a=32) and (a=2). Substitute when a coefficient is unknown.
Step 3
Exam Tip
(x=4) रखने पर (16a-40+8=0) इसलिए (16a=32) और (a=2)। अज्ञात गुणांक में प्रतिस्थापन करें।
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Question 3/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x=3) समीकरण \(ax^2-8x+6=0\) का मूल है तो (a) का मान क्या है?
If (x=3) is a root of \(ax^2-8x+6=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (9a-24+6=0), so (9a=18) and (a=2). Substitute in questions with an unknown coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=3) gives (9a-24+6=0), so (9a=18) and (a=2). Substitute in questions with an unknown coefficient.
Step 3
Exam Tip
(x=3) रखने पर (9a-24+6=0) इसलिए (9a=18) और (a=2)। अज्ञात गुणांक वाले प्रश्न में प्रतिस्थापन करें।
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Question 4/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (x=2) समीकरण \(ax^2-5x+2=0\) का मूल है तो (a) का मान क्या है?
If (x=2) is a root of \(ax^2-5x+2=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4a-10+2=0), so (4a=8) and (a=2). Substitute in questions with an unknown coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=2) gives (4a-10+2=0), so (4a=8) and (a=2). Substitute in questions with an unknown coefficient.
Step 3
Exam Tip
(x=2) रखने पर (4a-10+2=0) इसलिए (4a=8) और (a=2)। अज्ञात गुणांक वाले प्रश्न में प्रतिस्थापन करें।
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Question 5/6
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((k-1)x-2 +3x+2=0) द्विघात रहे इसके लिए कौन सी शर्त सही है?
Which condition is correct for ((k-1)x-2 +3x+2=0) to remain quadratic?
#quadratic equations
#parameter
#leading coefficient
A (k=1)
B \(k\neq1\)
C (k=0)
D (k=-1)
Explanation opens after your attempt
Correct Answer
B. \(k\neq1\)
Step 1
Concept
The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq1\). The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 3
Exam Tip
द्विघात पद का गुणांक ((k-1)) है जो (0) नहीं होना चाहिए। इसलिए \(k\neq1\) होना जरूरी है।
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Question 6/6
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस शर्त पर \(px^2+qx+r=0\) द्विघात समीकरण होगा?
Under which condition will \(px^2+qx+r=0\) be a quadratic equation?
#quadratic equations
#condition
#leading coefficient
A (p=0)
B \(p\neq0\)
C (q=0)
D (r=0)
Explanation opens after your attempt
Correct Answer
B. \(p\neq0\)
Step 1
Concept
The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 2
Why this answer is correct
The correct answer is B. \(p\neq0\). The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 3
Exam Tip
द्विघात पद \(px^2\) बना रहे इसलिए \(p\neq0\) होना चाहिए। यदि (p=0) हो तो घात (2) नहीं रहेगी।
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