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Quadratic Equations

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf ((r^2-49)x^2+(r+7)x+2=0) is a quadratic equation, what is the correct condition on (r)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Expert MathematicsWhat is the standard quadratic form of ((3x-2)(2x+5)=4(x+1))?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Expert MathematicsIf A = {x ∈ R | x² − 9 = 0} and B = {x ∈ R | x² − 6x + 9 = 0}, what is A ∪ B?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 10Medium MathematicsThe length of a rectangle is \\(2x+1\\) units and its breadth is \\(x-4\\) units. If its area is \\(45\\) square units, which quadratic equation represents this situation?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf (\alpha,\beta) are roots of (x^2-10x+q=0) and (\alpha^2+\beta^2=58), what is the value of (q)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf the roots of the equation \(x^2-2(k+1)x+k^2=0\) are real and distinct, what is the correct condition on \(k\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsWhat is the standard form with integer coefficients of (\frac{(x+1)^2}{2}+\frac{(x-3)^2}{3}=10)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf \(x^2-2ax+a^2-25=0\), what is the difference between the larger and smaller roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsThe equation \\(x^2+10x+k=0\\) has no real roots. What is the correct condition on \\(k\\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf α and β are roots of x² − 6x − 27 = 0, what is αβ + 3α + 3β?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 28Medium MathematicsIf \(\alpha\) and \(\beta\) are the roots of \(x^2-13x+36=0\), what is the value of \((\alpha+\beta)^2\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsA right triangle has a base of \((x+3)\) units, a height of \((x+7)\) units, and an area of 55 square units. Which quadratic equation represents this situation?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-12x+35=0\), what is the value of \((\alpha-5)(\beta-5)\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf the roots of (x^2+px+q=0) are (4) and (p), what is the value of (p)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsThe roots of the quadratic equation \(x^2-7x+3=0\) are \(\alpha\) and \(\beta\). What is the value of \(\alpha+\beta+3\alpha\beta\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf \(x=-1\) is a root of the quadratic equation \(x^2+(4k-1)x+3k=0\), what is the value of \(k\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsWhat is the standard form of ((x-3)^2+(x+4)^2=(x-1)^2)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf \(a=-2\), what type of statement does \((a+2)x^2+(a^2-4)x+7=0\) become?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsThe length of a rectangle is \(x+3\) cm and its breadth is \(x-2\) cm. If its area is \(40\) cm², which is the correct quadratic equation in \(x\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsWhat is the sum of cubes of the roots of (x^2-5x-14=0)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert