What is the perfect square form of (x^2-18x+81)?
Correct answer: A
(81=9^2) and (-18x=-2\cdot x\cdot9). In exams, identify the subtraction square from the negative middle term.
View question detailsMathematics
Quadratic expressions
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Hard · Level 73 · quadratic-expressions,perfect-square,minus
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- ((x-9)^2)
- ((x+9)^2)
- ((x-18)^2)
- ((x+81)^2)
Hard · Level 73 · quadratic-expressions,perfect-square,coefficient
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- ((4x+5)^2)
- ((16x+5)^2)
- ((4x-5)^2)
- ((2x+10)^2)
Hard · Level 73 · quadratic-expressions,unknown-coefficient,perfect-square
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- (7)
- (14)
- (49)
- (98)
Hard · Level 72 · quadratic expressions, factorisation, discriminant, algebraic identities, class 9 mathematics
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- \(x^2+5x+6\)
- \(2x^2+7x+3\)
- \(2x^2+3x+5\)
- \(3x^2-10x+3\)
Hard · Level 72 · quadratic expressions,completing square,hard
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- ((x-6)^2-16)
- ((x+6)^2-16)
- ((x-12)^2+20)
- ((x-6)^2+16)
Hard · Level 72 · quadratic expressions, algebraic identities, perfect square trinomial, factorisation, error analysis
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- \((x-5)(x+5)=x^2-25\) होता है; सही गुणनखंड \((x-5)^2\) है।
- मध्य पद का चिह्न गलत है; सही गुणनखंड \((x+5)^2\) है।
- स्थिर पद गलत है; सही गुणनखंड \((x-5)(x-25)\) है।
- व्यंजक का गुणनखंड नहीं किया जा सकता।
Hard · Level 73 · algebraic identities, quadratic expressions, difference of squares, factorisation, class 9 mathematics
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- \(p^2-16q^2\)
- \(p^2+16q^2\)
- \(p^2-8pq+16q^2\)
- \(p^2+8pq+16q^2\)
Hard · Level 73 · quadratic expressions,degree of polynomial,algebraic identities,class 9 mathematics
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- Its degree is 2
- All its coefficients are non-zero
- It has two distinct real zeros
- It can always be written as a product of two linear factors with integer coefficients
Hard · Level 73 · quadratic-expressions,factorisation,negative-middle
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- ((x-4)(x-8))
- ((x+4)(x+8))
- ((x-2)(x-16))
- ((x+2)(x+16))
Hard · Level 73 · quadratic-expressions,perfect-square,unknown-middle
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- (30)
- (60)
- (90)
- (150)
Hard · Level 74 · quadratic expressions, algebraic identities, polynomial degree, class 9 mathematics, expression classification
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- \(5x^2-3x\)
- \(5x^3-3x\)
- \(5x-3\)
- \(\frac{5}{x}-3\)
Hard · Level 74 · perfect square,negative middle term,quadratic
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- ((x+7)^2)
- ((x-14)^2)
- ((x+49)^2)
- ((x-7)^2)
Hard · Level 74 · algebraic identities,binomial square,quadratic expressions,polynomial expansion
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- \(4x^2-6x+9\)
- \(4x^2-12x+9\)
- \(2x^2-12x+9\)
- \(4x^2+12x+9\)
Hard · Level 74 · product of binomials,middle coefficient,quadratic
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- (7)
- (10)
- (3)
- (-10)
Hard · Level 74 · constant term,binomial product,quadratic
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- (21)
- (4)
- (-4)
- (-21)
Hard · Level 74 · value of expression,substitution,quadratic
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- (8)
- (10)
- (6)
- (4)
Hard · Level 74 · quadratic expressions,perfect square trinomial,algebraic identities,discriminant,grade 9 mathematics
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- \(b^2=4c\)
- \(b^2=2c\)
- \(b=2c\)
- \(b+c=0\)
Hard · Level 74 · completing square,negative coefficient,quadratic
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- (81)
- (36)
- (18)
- (324)
Hard · Level 74 · algebraic identities,quadratic expressions,perfect square trinomial,class 9 mathematics,polynomial identification
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- \(9x^2+12x+4\)
- \(9x^2+12x+2\)
- \(9x^2+8x+4\)
- \(9x^2-12x+4x\)
Hard · Level 74 · quadratic expressions,perfect square trinomial,algebraic identities,polynomials,class 9 mathematics
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- \(4x^2 - 12x + 9\)
- \(4x^2 - 12x + 8\)
- \(4x^2 - 9\)
- \(4x^2 + 12x + 8\)
In which form can (16x^2+40x+25) be written?
Correct answer: A
(16x^2=(4x)^2), (25=5^2), and (40x=2\cdot4x\cdot5). In exams, check the square roots of first and last terms.
View question details(x^2+mx+49) is a perfect square and (m) is positive. What will be the value of (m)?
Correct answer: B
(49=7^2), so the middle term is (2\cdot x\cdot7=14x). In exams, take the positive middle coefficient for a positive perfect square.
View question detailsWhich of the following quadratic expressions cannot be factorised into two linear expressions with integer coefficients?
Correct answer: C
For \(2x^2+3x+5\), the discriminant is \(b^2-4ac=3^2-4(2)(5)=-31\). Since it is negative, the expression has no real linear factors, hence no integer-coefficient factorisation. Exam tip: check the discriminant first.
View question detailsWrite (x^2-12x+20) in completed square form.
Correct answer: A
(x^2-12x+36=(x-6)^2) and (20=36-16). In exams take half of the middle coefficient and form its square.
View question detailsA student claims that \(x^2-10x+25\) factorises as \((x-5)(x+5)\). What is the error in the student's claim?
Correct answer: A
\((x-5)^2=x^2-2\cdot5x+5^2=x^2-10x+25\), so the correct factorisation is \((x-5)^2\). In contrast, \((x-5)(x+5)\) gives \(x^2-25\). Exam tip: check whether the middle term is \(\pm2ab\).
View question detailsWhich of the following quadratic expressions has conjugate linear binomial factors?
Correct answer: A
\(p^2-16q^2=p^2-(4q)^2=(p-4q)(p+4q)\), so its factors are conjugate binomials. C is a repeated-binomial square. Exam tip: spot two squares separated by a minus sign.
View question detailsWhich statement is always true about a quadratic polynomial \(ax^2+bx+c\), where \(a\ne0\)?
Correct answer: A
Since \(a\ne0\), the \(x^2\) term is present, so the highest power is 2. \(b\) or \(c\) may be zero, and real roots are not guaranteed. Exam tip: check the highest power first.
View question detailsWhat is the correct factorised form of (x^2-12x+32)?
Correct answer: A
(-4-8=-12) and ((-4)(-8)=32). In exams, use both negative signs when the constant is positive and middle term is negative.
View question details(25x^2+mx+36) is a perfect square and (m) is positive. What will be the value of (m)?
Correct answer: B
(25x^2=(5x)^2) and (36=6^2), so the middle term is (2\cdot5x\cdot6=60x). In exams, multiply twice the two square roots.
View question detailsWhich of the following is a quadratic expression in x even though it has no constant term?
Correct answer: A
In \(5x^2-3x\), the highest power of x is 2, so it is quadratic. A constant term is not compulsory. \(5x^3-3x\) is cubic because its highest power is 3. Exam tip: identify the degree from the highest exponent.
View question detailsIn which form can (x^2-14x+49) be written?
Correct answer: D
Since (49=7^2) and the middle term is (-14x), the form is ((x-7)^2). Exam tip: pay attention to the negative sign.
View question detailsWhat is the correct expansion of \((2x-3)^2\)?
Correct answer: B
Using \((a-b)^2=a^2-2ab+b^2\), take \(a=2x\) and \(b=3\). Then \((2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9\). Hence, option B is correct. Option A has an incorrect coefficient of the middle term, while option D has the wrong sign. Exam tip: the middle term in \((a-b)^2\) is always \(-2ab\).
View question detailsWhat will be the coefficient of (x) in ((x+5)(x-2))?
Correct answer: C
The expansion is (x^2+3x-10), so the coefficient of (x) is (3). Exam tip: the sum of constants gives the middle coefficient.
View question detailsWhat will be the constant term of ((x-7)(x+3))?
Correct answer: D
The constant term is ((-7)\cdot3=-21). Exam tip: multiply the constant numbers to get the constant term.
View question detailsIf (x=2), what is the value of (x^2+5x-6)?
Correct answer: A
We get (2^2+5\cdot2-6=8). Exam tip: do powers first, then multiplication, then addition and subtraction.
View question detailsWhich condition correctly identifies the quadratic expression \(x^2+bx+c\), with real coefficients, as a perfect-square trinomial?
Correct answer: A
For a perfect square, \(x^2+bx+c=(x+b/2)^2\). Thus the constant term must be \(b^2/4\), giving \(b^2=4c\). Exam tip: equivalently, check whether the discriminant \(b^2-4c\) is zero.
View question detailsWhat will (k) be to make (x^2-18x+k) a perfect square?
Correct answer: A
Half of (-18) is (-9), and ((-9)^2=81). Exam tip: the square becomes positive even with a negative sign.
View question detailsWhich of the following expressions is a perfect-square quadratic trinomial?
Correct answer: A
\(9x^2+12x+4=(3x)^2+2(3x)(2)+2^2=(3x+2)^2\), so it is a perfect square. In option B, the constant should be \(4\), not \(2\). Exam tip: match the middle term with \(2ab\).
View question detailsWhich of the following trinomials can be written as the product of two identical binomials?
Correct answer: A
Option A is \(4x^2-12x+9=(2x-3)^2=(2x-3)(2x-3)\), so it is the product of two identical binomials. Option B is the closest distractor, but \((2x-3)^2\) has constant term \(9\), not \(8\). Exam tip: for a perfect-square trinomial \(ax^2+bx+c\), check whether \(b^2=4ac\).
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