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Algebraic Identities

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhich of the following is a quadratic expression in x even though it has no constant term?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 74HardMathematicsWhich statement is always true about a quadratic polynomial \(ax^2+bx+c\), where \(a\ne0\)?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following quadratic expressions has conjugate linear binomial factors?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsA student claims that \(x^2-10x+25\) factorises as \((x-5)(x+5)\). What is the error in the student's claim?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 72HardMathematicsWhich of the following quadratic expressions cannot be factorised into two linear expressions with integer coefficients?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 72HardMathematicsWhich of the following quadratic expressions remains positive for every real value of x?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following expressions represents a quadratic polynomial in x?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf \(a,b,c\) are constants, which condition is necessary for \(p(x)=ax^2+bx+c\) to be called a quadratic expression?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf the quadratic expression \(x^2+px+16\) is a perfect square of a binomial, which statement about the possible values of \(p\) is correct?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich statement correctly gives the factors of the expression \(p^2-q^2\)?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf the quadratic expression \(ax^2+bx+c\), where \(a\ne 0\), is the square of a linear binomial, which of the following statements is always true?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf \(a,b,c\) are real numbers and \(a\ne0\), which condition is necessary and sufficient for \(ax^2+bx+c\) to be the square of a linear expression?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf a is any real number, which of the following expressions will always remain a quadratic expression in x?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf \(a,b,c\) are real numbers, when is \(ax^2+bx+c\) called a quadratic expression?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following quadratic expressions can be factorised as the product of two identical binomials?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following quadratic expressions can be written as the product of two identical linear factors?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf the quadratic expression \(x^2+px+q\) can be written as the product of two identical linear factors, which relation between \(p\) and \(q\) is necessary?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following factorizations correctly applies the identity for the difference of squares?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsWhich of the following quadratic expressions represents the square of a binomial?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73HardMathematicsIf a, b and c are constants, under which condition is \(ax^2+bx+c\) a quadratic expression in x?Class 9Exploring Algebraic IdentitiesQuadratic expressionsLevel 73Hard