Question

please tell me someone and explain me please ​

Answer 1

ANSWER

hope this helps you out

Answer 2

$\huge \red{ \fcolorbox{green}{grey}{required \: answer}}$

$\bold { \underline{ \underline \orange{answer}}} \orange →</p><p>$

(q-3) and (q-7)

$\bold { \underline{ \underline \orange{solution}}} \orange →</p><p>$

i) by Splitting the Middle term

$\bold {\color{yellow} {q}^{2} - 10q + 21} \\ \\ \bold{ \implies \: {q}^{2} - (7 + 3)q + 21 } \\ \\ \bold{ \implies \: {q}^{2} - 7q - 3q + 21} \\ \\ \bold{ \implies \: q(q - 7) - 3(q - 7)} \\ \\ \bold{ \implies \: (q - 3)(q - 7)} \: \: \: \: \: \: \: \: \: \:$

ii) by quadratic formula±

$\bold{{ \tt \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }}$

so here,

a = 1 , b = -10 and c = 21

$\bold{ { \tt \: q = \frac{ - ( - 10)± \sqrt{ {( - 10)}^{2} - 4 \times 21 \times 1 } }{2 \times 1} }}$

$\bold{{ \tt q = \frac{10± \sqrt{100 - 84} }{2} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \tt{ \implies q = \frac{10± \sqrt{16} }{2} } } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{{ \tt \implies \:q = \frac{10±4}{2} }} \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{{ \tt \: \implies q = \frac{10 - 4}{2} \: and \: q = \frac{10 + 4}{2} }} \\ \\ \bold{{ \tt \implies \: q = \frac{6}{2} \: \: \: and \: \: q = \frac{14}{2} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ { \tt \implies \: q = 3 \: \: and \: \: q = 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

→ q-3 = 0 and q-7 = 0

so factors of equation are (q-3) and (q-7)