(b) x2 + x – 5 = 0
Same as the previous one. Let’s check the discriminant value for distinct real roots.
a. Given, 2x2 - 3√2x + 9/4 = 0
∴ D = b2 - 4ac = 0
= (-3√2)2 - 4(2) (9/4)
= 18 - 18 = 0
Hence, the roots are real and equal.
b. Given, x2 + x – 5 = 0
∴ D = b2 - 4ac = 0
= (1)2 - 4(1) (-5)
= 1 + 20 = 21 > 0
Hence, the roots are real and distinct.
c. Given, x2 + 3x + 2√2 =0
∴ D = b2 - 4ac = 0
= 32 - 4(1) (2√2)
= 9 - 8√2 < 0
Hence, the roots are imaginary.
d. Given, 5x2 - 3x + 1 = 0
∴ D = b2 - 4ac = 0
= (-3)2 - 4(5)(1)
= 9 – 20 < 0
Hence, the roots are imaginary.
