Class 10th Maths notes
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Class 10th Maths notes (@class_10_math_notes) Ingliz til segmentidagi kanali faol ishtirokchi. Hozirda hamjamiyat 15 817 obunachidan iborat bo'lib, TaΚΌlim toifasida 12 937-o'rinni va Hindiston mintaqasida 25 334-o'rinni egallagan.
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15 817
Obunachilar
-1424 soatlar
-857 kun
-30530 kun
Postlar arxiv
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π QUIZ EXPLANATION
β Question: The roots of xΒ² - 4x + 4 = 0 are:
β
Correct Answer: 2, 2
π‘ Explanation:
The correct answer is 2, 2.
Reason - This factors as (x - 2)Β² = 0, giving a double root at x = 2.
Concept - This is a perfect square trinomial where both roots are the same, confirming that the discriminant is zero.
Fact - Using the quadratic formula: x = (4 Β± β(16-16))/2 = (4 Β± 0)/2 = 2, giving the repeated root x = 2.
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π QUIZ EXPLANATION
β Question: If the discriminant of a quadratic equation is zero, the roots are:
β
Correct Answer: Real and equal
π‘ Explanation:
The correct answer is Real and equal.
Reason - When Ξ = bΒ² - 4ac = 0, the quadratic formula gives x = -b/2a twice, resulting in one repeated real root.
Concept - This means the parabola touches the x-axis at exactly one point (the vertex), making it a perfect square trinomial.
Fact - Examples include xΒ² - 4x + 4 = 0, where Ξ = 16 - 16 = 0, giving the double root x = 2.
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If the discriminant of a quadratic equation is zero, the roots are:
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π QUIZ EXPLANATION
β Question: The discriminant of the quadratic equation axΒ² + bx + c = 0 is:
β
Correct Answer: bΒ² - 4ac
π‘ Explanation:
The correct answer is bΒ² - 4ac.
Reason - The discriminant (Ξ) is defined as bΒ² - 4ac and determines the nature of roots in the quadratic formula.
Concept - The discriminant tells us about the roots: if Ξ > 0 (two distinct real roots), Ξ = 0 (one repeated real root), or Ξ < 0 (no real roots).
Fact - This expression appears under the square root in the quadratic formula: x = (-b Β± β(bΒ² - 4ac))/2a.
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The discriminant of the quadratic equation axΒ² + bx + c = 0 is:
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π QUIZ EXPLANATION
β Question: The solution of x + y = 5 and x - y = 1 is:
β
Correct Answer: (3, 2)
π‘ Explanation:
The correct answer is (3, 2).
Reason - Adding the equations: (x + y) + (x - y) = 5 + 1 gives 2x = 6, so x = 3. Substituting: 3 + y = 5, so y = 2.
Concept - This uses the elimination method to solve simultaneous linear equations by eliminating one variable.
Fact - Verification: 3 + 2 = 5 β and 3 - 2 = 1 β, confirming that (3, 2) satisfies both equations.
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π QUIZ EXPLANATION
β Question: A pair of linear equations has unique solution when:
β
Correct Answer: aβ/aβ β bβ/bβ
π‘ Explanation:
The correct answer is aβ/aβ β bβ/bβ.
Reason - When the ratios of coefficients are unequal, the lines intersect at exactly one point, giving a unique solution to the system.
Concept - This condition ensures that the two linear equations represent different, non-parallel lines that must intersect at one point.
Fact - If aβ/aβ = bβ/bβ but β cβ/cβ, the lines are parallel (no solution), and if aβ/aβ = bβ/bβ = cβ/cβ, the lines are identical (infinitely many solutions).
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π QUIZ EXPLANATION
β Question: The zeroes of the polynomial xΒ² - 5x + 6 are:
β
Correct Answer: 2, 3
π‘ Explanation:
The correct answer is 2, 3.
Reason - Setting xΒ² - 5x + 6 = 0 and factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Concept - Zeroes are the values of x that make the polynomial equal to zero, and they correspond to the x-intercepts of the polynomial's graph.
Fact - This can be verified by substitution: (2)Β² - 5(2) + 6 = 4 - 10 + 6 = 0, and (3)Β² - 5(3) + 6 = 9 - 15 + 6 = 0.
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π QUIZ EXPLANATION
β Question: What is the degree of the polynomial 3xΒ² + 2x + 1?
β
Correct Answer: 2
π‘ Explanation:
The correct answer is 2.
Reason - The degree of a polynomial is the highest power of the variable, and in 3xΒ² + 2x + 1, the highest power of x is 2.
Concept - The degree determines many properties of the polynomial, including the maximum number of roots and the general shape of its graph.
Fact - This is a quadratic polynomial (degree 2), which means its graph is a parabola and it can have at most 2 real roots.
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π QUIZ EXPLANATION
β Question: The decimal expansion of a rational number is:
β
Correct Answer: Either terminating or non-terminating repeating
π‘ Explanation:
The correct answer is Either terminating or non-terminating repeating.
Reason - Rational numbers in decimal form either terminate (like 1/2 = 0.5) or have infinitely repeating patterns (like 1/3 = 0.333...).
Concept - The nature of decimal expansion depends on the prime factorization of the denominator when the fraction is in lowest terms - only factors of 2 and 5 give terminating decimals.
Fact - Examples include 3/4 = 0.75 (terminating) and 2/3 = 0.666... (non-terminating repeating), while irrational numbers like Ο have non-terminating, non-repeating expansions.
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π QUIZ EXPLANATION
β Question: Which of the following is an irrational number?
β
Correct Answer: β2
π‘ Explanation:
The correct answer is β2.
Reason - β2 is an irrational number because it cannot be expressed as a ratio of two integers and its decimal expansion is non-terminating and non-recurring.
Concept - Irrational numbers are real numbers that cannot be written as fractions (p/q where p and q are integers and q β 0).
Fact - 2/3 and 0.5 are rational numbers, while Ο/Ο = 1, which is also rational. Only β2 among the given options is irrational.
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