(a) Determine whether the quadratic equation912+71-2 0 has real roots.

1.	(a) Determine whether the quadratic equation912+71-2 0 has real roots. If so, find theroots by quadratic formula.
Answer» If a quadratic equation has real roots then the discriminant (b² - 4ac ) is a positive value. The given quadratic equation be, 9x^2 + 7x - 2 = 0 To find discriminant a = 9, b = 7 and c = -2 b² - 4ac = (7)² - (49-2) = 49 + 72 = 121 Therefore discriminantis positive. So, the equation 9x^2 +7x - 2 = 0 has real roots 9x^2 + 7x - 2 = 09x^2 + 9x - 2x - 2 = 09x(x + 1) - 2(x + 1) = 0(9x - 2)(x + 1) = 0x = 2/9, - 1 Hence, roots of equation are 2/9 and - 1

(a) Determine whether the quadratic equation912+71-2 0 has real roots. If so, find theroots by quadratic formula.

Answer»

If a quadratic equation has real roots then the discriminant (b² - 4ac ) is a positive value.

The given quadratic equation be, 9x^2 + 7x - 2 = 0

To find discriminant a = 9, b = 7 and c = -2

b² - 4ac = (7)² - (4*9*-2) = 49 + 72 = 121

Therefore discriminantis positive. So, the equation 9x^2 +7x - 2 = 0 has real roots

9x^2 + 7x - 2 = 09x^2 + 9x - 2x - 2 = 09x(x + 1) - 2(x + 1) = 0(9x - 2)(x + 1) = 0x = 2/9, - 1

Hence, roots of equation are 2/9 and - 1