Question

the difference between the roots of the equation X square - 13 x + K =0 is 7 find k​

Answer 1

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$\large\mathcal\red{solution}$

$\\if \: a \: and \: b \: are \: the \: zeroes \: of \: the \: quadratic \: equation\\ \: then \: the \: equation \: can \: be \: written \: as \: \\ x {}^{2} - (a + b)x + ab = 0 \\ here \: the \: given \: equation \: is \: \\ x {}^{2} - 13k + k = 0 \: \\ so \: the \: sum \: o \: th e\: \: equation \: is \: = 13 \: and \\ \: product \: of \: the \: roots \: or \: zeros \: is \: = k \\ therefore \: the \: difference \: of \:the \: zeros \: is \: \\ = \sqrt{(13) {}^{2} - 4k} \\ according \: to \: the \: question \: \\ \sqrt{(13) {}^{2} - 4k} = 7 \\ = > 13 {}^{2} - 4k = 7 {}^{2} \\ = > 4k = 13 {}^{2} - 7 {}^{2} \\ = > 4k = (13 + 7)(13 - 7) \\ = > k = \frac{20 \times 6}{4} \\ = > k = 30$

$\large\mathcal\red{hope\: this \: helps \:you......}$