Question

Find the roots of the following quadratic equations by factorisation: x^2 – 3x – 10 = 0. ( Note :- ^ represent the power of value mean ^2 mean square )​

Answer 1

$\sf{\underline{\boxed{\green{\large{\bold{ Question}}}}}}$

• solve the equation using factorisation $\sf x^2 - 3x - 10 = 0$

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$\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}$

$\sf\implies x^2 - 3x - 10 = 0$

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• arrange factors of 10 in such a way that the sum of them is the middle term .

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$\sf\implies x^2 - 5x + 2x - 10 = 0$

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$\sf\implies x( x - 5 ) + 2 ( x - 5 ) = 0$

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$\sf\implies ( x + 2 ) ( x - 5 ) = 0$

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$begin{tabular}{|c|c|}\cline{1-2}\sf ( x + 2 ) = 0 &\sf ( x - 5 ) = 0 \\\cline{1-2}\sf x = 0 - 2 &\sf x = 0 + 5 \\\cline{1-2}\sf x = -2 &\sf x = 5 \\\cline{1-2}\end{tabular}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = -2 \: or \: 5 }}}}}}$

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$\sf{\red{\boxed{\huge{\bold{Steps \: involved}}}}}$

• Clear all fractions and brackets , if necessary.
• Transport all the terms to the left hand side to get an equation in the form of $\sf{\bold{ ax^2 + bx + c = 0 }}$
• Factorise the expression on the left hand side .
• Put each factor to zero and solve.