Question

100 points
FACTORISE:-

${x}^{2} - 3x - 2$
NEED CORRECT EXPLANATION. ..... ....... ...​

Answer 1

Shirdharacharya Formula

→ x = (- b ± √D)/2a, where D = b² - 4ac.

Note that if

• D > 0 then real and distinct roots
• D = 0 then real and equal roots
• D < 0 then imaginary roots

→ x² - 3x - 2

→ D = (- 3)² - 4(1)(- 2)

→ D = 9 + 8

→ D = 17

→ x = [- (- 3) ± √17]/2(1)

→ x = (3 ± √17)/2

→ x² - 3x - 2 = [x - (3 + √17)/2][x - (3 - √17)/2]

Answer: [x-(3+√17)/2][x-(3-√17)/2]

Answer 2

Solution:

Given equation ;

x² - 3x - 2 = 0

On comparing the given equation with ax² + bx + c = 0, we get -

• a = 1
• b = - 3
• c = - 2

Discriminant = b² - 4ac

⇒ D = (-3)² - 4 * 1 * (-2)

⇒ D = 9 + 8

⇒ D = 17

$\tt x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ \rightarrow \tt x = \frac{ - ( - 3) \pm \sqrt{17} }{2 \times 1} \\ \\ \rightarrow \tt x = \frac{3 \pm \sqrt{17} }{2}$

Therefore,

$\boxed{\bf x = \frac{3 + \sqrt{17} }{2} \: or \: x = \frac{3 - \sqrt{17} }{2}}$

Factorisation ;

⇒ x² - 3x - 2

⇒ $\sf \left[\dfrac{x - (3+\sqrt{17})}{2}\right] \left[\dfrac{x - ( 3 - \sqrt{17})}{2} \right]$