Question

solve the following into factors :- 2-a-a²​

Answer 1

Answer:

$(a - \frac{1}{2} )and \: (a + \frac{5}{2} )$

SOLUTION :-

Given equation ,

$2 - a - {a}^{2} = 0$

Multiplying by (-1) on both sides ,

${a}^{2} + a - 2 = 0 \\ \\ a = - 1 +or - \frac{ \sqrt{ {1}^{2} - 4(1)( - 2)} }{2(1)} \\ \\ a = - 1+or - \frac{ \sqrt{9} }{2} \\ \\ a = - 1+or - \frac{3}{2} \\ \\ a = \frac{ - 5}{2} \: \: or \: a = \frac{1}{2} \\ \\ therefore \: \: factors \: \: are \: \: (a - \frac{1}{2} )and \: (a + \frac{5}{2} )$

NOTE :-

• If ax^2 + bx + c represents a quadratic equation then roots are given by
• $x = - b \: + or - \frac{ \sqrt{ {b}^{2} - 4ac } }{2a}$
• Here after multiplying both sides with (-1),
• a = 1
• b = 1
• c = -2