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Roots Of A Quadratic Equation

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 \(x^2-9x+18=0\), what is the value of \((\alpha-2)(\beta-2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of the equation \(x^2+px+18=0\) are in the ratio \(1:2\) and both roots are negative, what is the value of \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf α and β are roots of x² + 4x − 21 = 0, what is the value of |α − β|?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf 8\alpha9 and 8\beta9 are the roots of 8x^2-6x+5=09, what is the sum of 8\alpha+39 and 8\beta+39?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf α and β are roots of x^2-4x+3=0, which equation has 3α and 3β as roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the difference between the roots of x² - 7x + q = 0 is 1, what is the value of q?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of x² + px + 25 = 0 are equal and both negative, what is the value of p?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf roots of x² − (a+2)x + 2a = 0 are 2 and a, which reason is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf the roots of (x^2-(m+3)x+18=0) are (3) and (6), what is the value of (m)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-6x+8=0\), what is the value of \(\alpha^2\beta^2\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf 2 and −3 are the roots of the equation \(3x^2+px+q=0\), what is the value of \(\frac{q}{3}\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of x² + px + 12 = 0 are in the ratio 1:3 and both are negative, what is p?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf α and β are roots of x² − 3x + 2 = 0, which equation has 2α and 2β as roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the difference of roots of (x^2-5x+q=0) is (1), what is the value of (q)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of x² − (a + 1)x + a = 0 are 1 and a, why is this correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf x = 4 is a root of ax² − 10x + 8 = 0, what is the value of a?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat is the sum of the squares of the roots of the equation \(x^2-9x+14=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf α and β are roots of 6x² + 5x − 4 = 0, what is αβ?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf the roots of a quadratic equation are 6 and 1/6, which statement is correct about them?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf both roots of the equation \(x^2+px+36=0\) are \(-6\), what is the value of \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium