(A) Given the quadratic equation: $x^{2} - 7 = 0$. We can rewrite this as: $x^{2} - (\sqrt{7})^{2} = 0$. Using the algebraic identity $a^{2} - b^{2} =

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(A) Given the quadratic equation: $x^{2} - 7 = 0$. We can rewrite this as: $x^{2} - (\sqrt{7})^{2} = 0$. Using the algebraic identity $a^{2} - b^{2} = (a - b)(a + b)$,we get: $(x - \sqrt{7})(x + \sqrt{7}) = 0$. Setting each factor to zero: $x - \sqrt{7} = 0 \implies x = \sqrt{7}$. $x + \sqrt{7} = 0 \implies x = -\sqrt{7}$. Thus,the solutions are $x = \sqrt{7}$ and $x = -\sqrt{7}$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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Solve the following equation using the method of factorization: $x^{2} - 7 = 0$.

A
$-\sqrt{7}, \sqrt{7}$
B
$\sqrt{7}, \sqrt{7}$
C
$\sqrt{7}, -\sqrt{7}$
D
$-\sqrt{7}, -\sqrt{7}$

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Mix Examples - Quadratic Equations

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Solve the following equation using the method of factorization: $x^{2} - 7 = 0$.

Similar Questions

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0$; $x = \frac{\sqrt{3}}{4}$.

Find the discriminant of the following quadratic equation: $9x^{2} - bx + 3 = 0$.

Solve the following equation using the method of factorization and write its solution set: $\frac{1}{x-2}+\frac{1}{x+3}=\frac{7}{2x}$ $(x \neq 2, x \neq -3, x \neq 0)$

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