Question

quadratic equation ​

Answer 1

Answer:

x^2-10x-24

x^2-12x+2x-24

x(x-12)+2(x-12)

(x-12)(x+2)

x=12 or x=-2

Answer 2

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

• solve the equation $\sf x^2 - 10x - 24 = 0$

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

$\sf\implies x^2 - 10x - 24 = 0$

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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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$\sf\implies x^2 - 12x + 2x - 24 = 0$

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$\sf\implies x( x - 12 ) + 2 ( x - 12 ) = 0$

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$\sf\implies ( x - 12 ) ( x + 2 ) = 0$

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$begin{tabular}{|c|c|}\cline{1-2}\sf ( x + 2 ) = 0 &\sf ( x - 12 ) = 0 \\\cline{1-2}\sf x = 0 - 2 &\sf x = 0 + 12 \\\cline{1-2}\sf x = -2 &\sf x = 12 \\\cline{1-2}\end{tabular}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = -2 \: or \: 12 }}}}}}$

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$\sf{\red{\boxed{\huge{\bold{Extra \: information}}}}}$

• An equation with one variable , in which the highest power of the variable is two , ia known as quadratic equation .
• The standard form of the quadratic form of a quadratic equation $\sf{\bold{ax^2 +bx + c = 0 }}$ , where a , b and c are all real numbers .