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CBSE 10th Mathematics | Irrational Numbers and Solved Examples
IRRATIONAL NUMBERS All real numbers which are not rational are called irrational numbers. $latex \displaystyle \sqrt{2}$, $latex \displaystyle \sqrt[3]{3}$, $latex \displaystyle -\sqrt{5}$ are some examples of irrational numbers. There are decimals which are non-terminating and non-recurring decimal. Example: 0.303003000300003… Hence, we can conclude that An irrational number is a non-terminating…
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CBSE 10th Mathematics | Solution of a Quadratic Equation by Completing the Square
Solution of a Quadratic Equation by Completing the Square Following steps are involved in solving a quadratic equation by quadratic formula · Consider the equation $latex \displaystyle a{{x}^{2}}+bx+c=0$, where a ¹ 0 · Dividing throughout by 'a', we get $latex \displaystyle {{x}^{2}}+\frac{b}{a}x+\frac{c}{a}=0$ · Add and subtract $latex \displaystyle {{\left( \frac{1}{2}\,\,\text{coefficient}\,\,\text{of}\,\,x \right)}^{2}}$, we get…
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CBSE 10th Mathematics | Nature of Roots of a Quadratic Equation
Nature of Roots of a Quadratic Equation In previous section, we have studied that the roots of the equation $latex \displaystyle a{{x}^{2}}+bx+c=0$ are given by $latex \displaystyle x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ A quadratic equation $latex \displaystyle a{{x}^{2}}+bx+c=0$ has · Two distinct real roots if $latex \displaystyle {{b}^{2}}-4ac>0$. If $latex \displaystyle {{b}^{2}}-4ac>0,$ we get…
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