Question

What is positive rootfor 'a' in the quadratic equation 6a^2-54a-1932=0

Answer 1

$Given \: Quadratic \: equation : \\6a^{2} - 54a - 1932 = 0$

/* Dividing each term by 6 , we get */

$\implies a^{2} - 9a - 322 = 0$

/* Splitting the middle term,we get */

$\implies a^{2} + 14a - 23a - 14 \times 23 = 0$

$\implies a( a + 14 ) - 23( a + 14 ) = 0$

$\implies (a+14)(a-23) = 0$

$\implies a+14= 0 \:Or \:a-23 = 0$

$\implies a = -14 \:Or \:a = 23$

Therefore.,

$\red{ The \: positive \:root \:of \:the \: equation}\\\green {= 23 }$

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