Question

Solve the following quadratic equation by factorisation method...
x^2 - 10x - 24=0​

Answer 1

$\huge{ Solution- }$

x^2 - 10x - 24 = 0

x^2 - (12 -2)x - 24 = 0

x^2 - 12x + 2x - 24 = 0

x (x - 12) + 2 (x - 12) = 0

(x - 12) (x + 2) = 0

x = 12 and x = -2

Answer 2

Answer:

$\huge{\red{\boxed{\boxed{\green{\sf{x=-2,12}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}}$

$\huge{\red{\boxed{\boxed{\green{\underline{\pink{\sf{MIDDLE\:TERM\:SPLITING-}}}}}}}}$

${x}^{2} - 10x - 24 = 0 \\ > > split \: 24 \: in \: two \: parts \: such \: that \: it \\ would \: be \: suitable \: for \: middle \: term \\ = ){x}^{2} - 12 x + 2x - 24 = 0 \\ = )x(x - 12) + 2(x - 12) = 0 \\ = )(x + 2)(x - 12) = 0 \\x + 2 = 0 \\ = )x = - 2 - - - - - 1st \: zeroes \\ = ) x - 12 = 0 \\ = ) x = 12 - - - - - 2nd \: zeroes$

$\huge{\red{\boxed{\boxed{\green{\underline{\pink{\sf{QUADRATIC\:FORMULA-}}}}}}}}$

$d = {b}^{2} - 4ac \\ d = ({ - 10})^{2} - 4(1 \times - 24) \\d = 100 + 96 \\ d = 196 \\ \\ x = \frac{ - b + - \sqrt{d} }{2a} \\ x = \frac{ - ( - 10) + \sqrt{196} }{2} \\ x = \frac{10 + 14}{2} \\ x = \frac{24}{2} \\ x = 12 - - - - - 1st \: zeroes \\ \\ x = \frac{10 - 14}{2} \\ x = \frac{ - 4}{2} \\ x = - 2-----2nd\:zeroes$

$\huge{\red{\boxed{\boxed{\green{\sf{x=-2,12}}}}}}$

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