Question

Find value of a x^2 - ax + a +2 has equal roots

Answer 1

Discriminant = b² - 4ac

Here,
a = 1
b = a
c = a + 2

Hence,
Discriminant = b² - 4ac

=> (a)² - 4(1)(a + 2)

=> a² - 4a - 8

Now,

a = 1
b = -4
c = -8

Discriminant = (-4)^2 - 4(1)(-8)
=> 16 + 32
=> 48

Using quadratic equation :

$a = \frac{ - ( - 4) + \sqrt{48} }{2(1)} \: \: \: or \: \: \: \: a = \frac{ - ( - 4) - \sqrt{48} }{2(1)} \\ \\ \\ => a = \frac{4 + \sqrt{4 \times 12} }{2} \: \: \: \: or \: \: \: \: \: a = \frac{4 - \sqrt{4 \times 12} }{2} \\ \\ \\ => a = \frac{4 + 2 \sqrt{12} }{2} \: \: \: or \: \: \: a = \frac{4 - 2 \sqrt{12} }{2} \\ \\ \\ => a = 2 + \sqrt{12} \: \: \: \: \: or \: \: a = 2 - \sqrt{12}$