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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 \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+14=0\), what is the value of \((\alpha+\beta)^2\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsA right triangle has a base of (x+2) units and a height of (x+6) units. If its area is 40 square units, which quadratic equation in x is correct?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf (\alpha,\beta) are the roots of the equation (x^2-9x+20=0), what is the value of (\alpha-4)(\beta-4)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf the roots of (x^2+px+q=0) are (2) and (p), which relation involving (q) is correct?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsThe roots of the equation \\(x^2-5x+2=0\\) are \\(\\alpha\\) and \\(\\beta\\). What is the value of \\(\\alpha+\\beta+2\\alpha\\beta\\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf \(x=-2\) is a root of the equation \(x^2+(3k+1)x+2k=0\), what is the value of \(k\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsWhat is the standard form of ((x+2)^2+(x-5)^2=(x+1)^2)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf \(a=2\), what type of statement does \((a-2)x^2+(a^2-4)x+5=0\) become?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsWhich of the following quadratic equations has one root \(x=0\) and the other root negative?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf the roots of the quadratic equation \(x^2+bx+c=0\) are \(-3\) and \(8\), what is the value of \(b+c\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsWhat is the sum of cubes of the roots of (x^2-3x-10=0)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf in \(3x^2+kx+12=0\), the product of roots is (-2) times the sum of roots, what is (k)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsWhich quadratic equation has sum of roots (0) and product (-81)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf (x=-1) is not a root of (kx^2+3x+2=0), what condition must (k) satisfy?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsThe roots of (x^2+px+16=0) are equal and positive. What is the value of (p)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf one root of (x^2+mx+25=0) is the reciprocal of the other, what can be said about (m)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf \(k\) is a real constant, what is the nature of the roots of the equation \(9x^2+12kx+4k^2=0\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf \\(x+a\\)^2 = x^2 - 12x + 36 holds for all real x, what is the value of a?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsWhich of the following quadratic equations will have two equal and negative roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30HardMathematicsIf (\alpha,\beta) are roots of (x^2-7x+12=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30Hard

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