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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 \(\alpha+\beta=10\) and \(\alpha\beta=21\), what are the zeros (roots)?Class 10PolynomialsIrrational numbers and real numbersLevel 27Expert MathematicsIf the zeroes of p(x) = x² − 2kx + 20 are k + √5 and k − √5, what is the positive value of k?Class 10PolynomialsIrrational numbers and real numbersLevel 27Hard MathematicsWhich quadratic polynomial has zeros \(2+\sqrt{10}\) and \(2-\sqrt{10}\)?Class 10PolynomialsIrrational numbers and real numbersLevel 27Expert MathematicsIf the zeros of a quadratic polynomial are \(5+\sqrt{3}\) and \(5-\sqrt{3}\), what is their product?Class 10PolynomialsIrrational numbers and real numbersLevel 26Expert MathematicsIf the zeroes of a monic quadratic polynomial are \(a+\sqrt{b}\) and \(a-\sqrt{b}\), what is its discriminant?Class 10PolynomialsIrrational numbers and real numbersLevel 25Expert MathematicsIf \(p(x)=x^2-6\sqrt{2}x+17\), what is the difference between its zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 25Expert MathematicsIf \(p(x)=x^2-2\sqrt{2}x+1\), what is the type of its zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 25Expert MathematicsIf \(p(x)=x^2-(3+\sqrt{2})x+3\sqrt{2}\), which is the correct pair of zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 25Expert MathematicsIf \(p(x)=x^2-2x+5\), why are its zeroes not real?Class 10PolynomialsIrrational numbers and real numbersLevel 27Hard MathematicsFor which value of \(k\) will the zeroes of \(x^2-2x+k\) be real and irrational?Class 10PolynomialsIrrational numbers and real numbersLevel 27Hard MathematicsIf the zeros of a quadratic polynomial are (5+\sqrt{2}) and (5-\sqrt{2}), what is the polynomial in standard form?Class 10PolynomialsIrrational numbers and real numbersLevel 27Hard MathematicsIf the zeros of the quadratic \(x^2-4x+r\) are rational, is the statement true when \(r=3\)?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf p(x)=\sqrt{3}x^2-6x+2\sqrt{3}, what is the product of its zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf \(p(x)=x^2-3x+\sqrt{2}\), what is the product of its zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf \(p(x)=x^2+2\sqrt{3}x+3\), what are its zeros?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf p(x) = x² + 6x + 7, what type of zeroes does it have?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 26Hard MathematicsIf the zeros of \(p(x)=x^2-6x+n\) are \(3+\sqrt{m}\) and \(3-\sqrt{m}\), and \(n=5\), what is the value of \(m\)?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf the zeros of \(f(x)=x^2+px+q\) are \(7+\sqrt{13}\) and \(7-\sqrt{13}\), what is the value of \(p+q\)?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard MathematicsIf \(p(x)=x^2-2\sqrt{3}x+2\), what is the product of its zeros?Class 10PolynomialsIrrational numbers and real numbersLevel 28Hard MathematicsIf \(p(x)=x^2-2x-3\), are both of its zeroes real?Class 10PolynomialsIrrational numbers and real numbersLevel 28Hard