Page 6 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

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Evidently, the roots are irrational (real) and unequal.
(b) 2x2 - x + 1 = 0
Here a = 2 , b = -1 and c = 1
Disc. = b2 - 4ac
= (-1)2 - 4(2) (1) = 1 - 8 = -7 < 0
As the Disc. is negative, therefore, the roots of the equation are
imaginary and unequal. Verification by solving the equation.
2x2 - x + 1 = 0
Using quadratic formula

Version 1.1 Evidently, the roots are imaginary and unequal.
(c) x2 + 8x + 16 = 0
Here a = 1, b = 8 and c = 16
Disc. = b2 - 4ac
= (8)2 - 4(1) (16)
= 64 - 64 = 0
As the discriminant is zero, therefore the roots are rational (real)
and equal.
Verification by solving the equation.
x2 + 8x + 16 = 0
(x + 4)2 = 0
⇒ x = -4, -4
So the roots are rational (real) and equal.
(d) 7x2 + 8x + 1 = 0
Here a = 7, b = 8 and c = 1
Disc. = b2 - 4ac
= (8)2 - 4(7) (1)
= 64 - 28 = 36 = (6)2
which is positive and perfect square.
∴ The roots are rational (real) and unequal.

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